Magma V2.7-1 Mon Jan 29 2001 02:55:44 on modular [Seed = 2161008971] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2002 and weight 2.... I. Manin symbols list. (0.08 s) II. 2-term relations. (1.251 s) III. 3-term relations. Computing quotient by 1344 relations. Form quot and then images (1.069 s) (total time to create space = 2.43 s) Computing cuspidal part of Full Modular symbols space of level 2002, weight 2, and dimension 344 Computing new part of Modular symbols space of level 2002, weight 2, and dimension 329. Computing 2-new part of Modular symbols space of level 2002, weight 2, and dimension 329. Computing space of modular symbols of level 1001 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.4 s) III. 3-term relations. Computing quotient by 448 relations. Form quot and then images (0.209 s) (total time to create space = 0.641 s) Computing index-1 degeneracy map from level 2002 to 1001. (2.149 s) Computing index-2 degeneracy map from level 2002 to 1001. (2.1 s) Computing index-1 degeneracy map from level 1001 to 2002. (1.09 s) Computing index-2 degeneracy map from level 1001 to 2002. (1.26 s) Computing DualVectorSpace of Modular symbols space of level 2002, weight 2, and dimension 329. Computing complement of Modular symbols space of level 2002, weight 2, and dimension 329 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 15. Goal dimension = 15. Computing T_2 on space of dimension 344. (0.21 s) Computing T_2 on dual space of dimension 15. T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^15 - 22*x^14 + 224*x^13 - 1400*x^12 + 6006*x^11 - 18732*x^10 + 43876*x^9 - 78592*x^8 + 108545*x^7 - 115598*x^6 + 94164*x^5 - 57624*x^4 + 25648*x^3 - 7840*x^2 + 1472*x - 128 p = %o, dimension = %o. 2 70 Computing T_3 on space of dimension 344. (0.179 s) Computing T_3 on dual space of dimension 15. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^15 - 60*x^14 + 1680*x^13 - 29120*x^12 + 349440*x^11 - 3075072*x^10 + 20500480*x^9 - 105431040*x^8 + 421724160*x^7 - 1312030720*x^6 + 3148873728*x^5 - 5725224960*x^4 + 7633633280*x^3 - 7046430720*x^2 + 4026531840*x - 1073741824 p = %o, dimension = %o. 3 15 Computing complement of Modular symbols space of level 2002, weight 2, and dimension 15 Computing 7-new part of Modular symbols space of level 2002, weight 2, and dimension 329. Computing space of modular symbols of level 286 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.14 s) III. 3-term relations. Computing quotient by 168 relations. Form quot and then images (0.079 s) (total time to create space = 0.23 s) Computing index-1 degeneracy map from level 2002 to 286. (0.251 s) Computing index-7 degeneracy map from level 2002 to 286. (0.451 s) Computing index-1 degeneracy map from level 286 to 2002. (1.281 s) Computing index-7 degeneracy map from level 286 to 2002. (1.349 s) Computing 11-new part of Modular symbols space of level 2002, weight 2, and dimension 329. Computing space of modular symbols of level 182 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.1 s) III. 3-term relations. Computing quotient by 112 relations. Form quot and then images (0.04 s) (total time to create space = 0.141 s) Computing index-1 degeneracy map from level 2002 to 182. (0.169 s) Computing index-11 degeneracy map from level 2002 to 182. (0.54 s) Computing index-1 degeneracy map from level 182 to 2002. (1.32 s) Computing index-11 degeneracy map from level 182 to 2002. (1.521 s) Computing 13-new part of Modular symbols space of level 2002, weight 2, and dimension 329. Computing space of modular symbols of level 154 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.089 s) III. 3-term relations. Computing quotient by 96 relations. Form quot and then images (0.031 s) (total time to create space = 0.12 s) Computing index-1 degeneracy map from level 2002 to 154. (0.149 s) Computing index-13 degeneracy map from level 2002 to 154. (0.59 s) Computing index-1 degeneracy map from level 154 to 2002. (1.179 s) Computing index-13 degeneracy map from level 154 to 2002. (1.821 s) Finding newform decomposition of Modular symbols space of level 2002, weight 2, and dimension 329. Computing cuspidal part of Modular symbols space of level 2002, weight 2, and dimension 329 Decomposing space of level 2002 and dimension 61 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 61. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^61 + 4*x^60 - 116*x^59 - 480*x^58 + 6302*x^57 + 27144*x^56 - 212944*x^55 - 962192*x^54 + 5010405*x^53 + 23990228*x^52 - 87035576*x^51 - 447503600*x^50 + 1153452810*x^49 + 6485404136*x^48 - 11861474612*x^47 - 74854172880*x^46 + 94957758250*x^45 + 699772328344*x^44 - 582967394460*x^43 - 5360203942016*x^42 + 2595878375062*x^41 + 33903492415240*x^40 - 6699435260552*x^39 - 177909415235472*x^38 - 7781059681283*x^37 + 776244487244884*x^36 + 195508873024904*x^35 - 2815702696489488*x^34 - 1228278140096410*x^33 + 8470070905624984*x^32 + 5123738291791956*x^31 - 21022279924850032*x^30 - 16102403404518774*x^29 + 42688797496374712*x^28 + 39651469532982908*x^27 - 70002076861871552*x^26 - 77519497860554214*x^25 + 90800597502490936*x^24 + 120445864176620856*x^23 - 89915908334120752*x^22 - 147685576230993339*x^21 + 63207400116401140*x^20 + 140838532270156000*x^19 - 25242680273713200*x^18 - 101997747769943442*x^17 - 2407661477476200*x^16 + 53995569003797388*x^15 + 10786934838703504*x^14 - 19556876124672431*x^13 - 7303122163434060*x^12 + 4206690347707312*x^11 + 2560880740958016*x^10 - 302719037117184*x^9 - 462839281222656*x^8 - 62849832382464*x^7 + 28707040641024*x^6 + 10893049331712*x^5 + 1364390313984*x^4 + 58888028160*x^3 time = 1.49 Factoring characteristic polynomial. [ , , , , , , , , , , , , , , , ] time = 0.089 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Charpoly = x^3 + x^2 - x - 1. Decomposing space of level 2002 and dimension 3 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^3 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Charpoly = x^3 + 3*x^2 - 9*x - 27. Decomposing space of level 2002 and dimension 3 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 3. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^3 - 8*x^2 + 20*x - 16 time = 0.01 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 4. Cutting out subspace using f(T_5), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Charpoly = x^2 - 14*x + 49. Decomposing space of level 2002 and dimension 2 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Charpoly = x^2 + 6*x + 9. Decomposing space of level 2002 and dimension 2 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). Charpoly = x^2 + 16*x + 64. Decomposing space of level 2002 and dimension 2 using T_17. (will stop at 672) Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing characteristic polynomial of T_17. x^2 + 2*x - 8 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_17), where f=x - 2. Cutting out subspace using f(T_17), where f=x + 4. Cutting out subspace using f(T_3), where f=x^2 - x - 3. Cutting out subspace using f(T_3), where f=x^2 + x - 3. Cutting out subspace using f(T_3), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Charpoly = x^4 - 6*x^3 - 17*x^2 + 78*x - 11. Decomposing space of level 2002 and dimension 4 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^4 + 2*x^3 - x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Charpoly = x^4 - 2*x^3 - 3*x^2 + 4*x - 1. Decomposing space of level 2002 and dimension 4 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing characteristic polynomial of T_5. x^4 + 2*x^3 - x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x^2 + x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Charpoly = x^4 - 28*x^2 + 16. Decomposing space of level 2002 and dimension 4 using T_17. (will stop at 672) Computing T_17 on dual space of dimension 4. T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing characteristic polynomial of T_17. x^4 - 4*x^3 - 21*x^2 + 50*x + 55 time = 0 Factoring characteristic polynomial. [ , ] time = 0.009 Cutting out subspace using f(T_17), where f=x^2 - 5*x - 5. Cutting out subspace using f(T_17), where f=x^2 + x - 11. Cutting out subspace using f(T_3), where f=x^2 + 3*x + 1. Cutting out subspace using f(T_3), where f=x^3 - 3*x^2 - 7*x + 20. Cutting out subspace using f(T_3), where f=x^3 - x^2 - 5*x + 4. Cutting out subspace using f(T_3), where f=x^3 + 3*x^2 - x - 4. Cutting out subspace using f(T_3), where f=x^4 + 2*x^3 - 5*x^2 - 10*x - 1. Cutting out subspace using f(T_3), where f=x^4 + 2*x^3 - 5*x^2 - 6*x - 1. Cutting out subspace using f(T_3), where f=x^5 - 4*x^4 - 7*x^3 + 36*x^2 - x - 52. Cutting out subspace using f(T_3), where f=x^5 - 4*x^4 - x^3 + 14*x^2 - 3*x - 8. Cutting out subspace using f(T_3), where f=x^5 - 13*x^3 - 2*x^2 + 41*x + 16. Cutting out subspace using f(T_3), where f=x^5 + 2*x^4 - 11*x^3 - 16*x^2 + 21*x + 16. Cutting out subspace using f(T_3), where f=x^5 + 2*x^4 - 7*x^3 - 8*x^2 + 13*x + 4. Cutting out subspace using f(T_3), where f=x^6 - 15*x^4 + 51*x^2 - 48. Computing representation of Modular symbols space of level 2002, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x p = %o, dimension = %o. 3 2 Computing T_5 on space of dimension 344. (0.24 s) Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 2 p = %o, dimension = %o. 5 2 Computing T_7 on space of dimension 344. (0.349 s) Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 2 p = %o, dimension = %o. 5 2 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^2 - x - 3 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^2 + x - 3 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^2 + x - 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^2 + x - 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^2 + 3*x + 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^3 - 3*x^2 - 7*x + 20 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - x^2 - 5*x + 4 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^3 + 3*x^2 - x - 4 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^4 + 2*x^3 - 5*x^2 - 10*x - 1 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^4 + 2*x^3 - 5*x^2 - 6*x - 1 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^5 - 4*x^4 - 7*x^3 + 36*x^2 - x - 52 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^5 - 4*x^4 - x^3 + 14*x^2 - 3*x - 8 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). %o x^5 - 13*x^3 - 2*x^2 + 41*x + 16 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^5 + 2*x^4 - 11*x^3 - 16*x^2 + 21*x + 16 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 p = %o, dimension = %o. 2 30 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). %o x^5 + 2*x^4 - 7*x^3 - 8*x^2 + 13*x + 4 p = %o, dimension = %o. 3 5 Computing representation of Modular symbols space of level 2002, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^6 - 6*x^5 + 15*x^4 - 20*x^3 + 15*x^2 - 6*x + 1 p = %o, dimension = %o. 2 31 Computing T_3 on dual space of dimension 6. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). %o x^6 - 15*x^4 + 51*x^2 - 48 p = %o, dimension = %o. 3 6 Computing cuspidal part of Full Modular symbols space of level 1001, weight 2, and dimension 116 Computing cuspidal part of Modular symbols space of level 1001, weight 2, and dimension 109 Computing new part of Modular symbols space of level 1001, weight 2, and dimension 109. Computing 7-new part of Modular symbols space of level 1001, weight 2, and dimension 109. Computing space of modular symbols of level 143 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.051 s) III. 3-term relations. Computing quotient by 56 relations. Form quot and then images (0.019 s) (total time to create space = 0.071 s) Computing index-1 degeneracy map from level 1001 to 143. (0.049 s) Computing index-7 degeneracy map from level 1001 to 143. (0.099 s) Computing index-1 degeneracy map from level 143 to 1001. (0.381 s) Computing index-7 degeneracy map from level 143 to 1001. (0.409 s) Computing DualVectorSpace of Modular symbols space of level 1001, weight 2, and dimension 109. Computing complement of Modular symbols space of level 1001, weight 2, and dimension 109 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 116. (0.02 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^7 - 21*x^6 + 189*x^5 - 945*x^4 + 2835*x^3 - 5103*x^2 + 5103*x - 2187 p = %o, dimension = %o. 2 7 Computing complement of Modular symbols space of level 1001, weight 2, and dimension 7 Computing 11-new part of Modular symbols space of level 1001, weight 2, and dimension 109. Computing space of modular symbols of level 91 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.029 s) III. 3-term relations. Computing quotient by 40 relations. Form quot and then images (0.009 s) (total time to create space = 0.049 s) Computing index-1 degeneracy map from level 1001 to 91. (0.029 s) Computing index-11 degeneracy map from level 1001 to 91. (0.159 s) Computing index-1 degeneracy map from level 91 to 1001. (0.391 s) Computing index-11 degeneracy map from level 91 to 1001. (0.389 s) Computing 13-new part of Modular symbols space of level 1001, weight 2, and dimension 109. Computing space of modular symbols of level 77 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.019 s) III. 3-term relations. Computing quotient by 32 relations. Form quot and then images (0.009 s) (total time to create space = 0.039 s) Computing index-1 degeneracy map from level 1001 to 77. (0.029 s) Computing index-13 degeneracy map from level 1001 to 77. (0.19 s) Computing index-1 degeneracy map from level 77 to 1001. (0.411 s) Computing index-13 degeneracy map from level 77 to 1001. (0.52 s) Decomposing space of level 1001 and dimension 59 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 59. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^59 + 3*x^58 - 89*x^57 - 267*x^56 + 3740*x^55 + 11212*x^54 - 98728*x^53 - 295504*x^52 + 1837558*x^51 + 5485482*x^50 - 25658122*x^49 - 76294022*x^48 + 279233202*x^47 + 825750366*x^46 - 2429215958*x^45 - 7130964018*x^44 + 17192971851*x^43 + 49986275137*x^42 - 100238859987*x^41 - 287853745033*x^40 + 485715512428*x^39 + 1373206280116*x^38 - 1968314674568*x^37 - 5457210265408*x^36 + 6698468129077*x^35 + 18128251094359*x^34 - 19190113985105*x^33 - 50417078101123*x^32 + 46322582934972*x^31 + 117388202823772*x^30 - 94164455223600*x^29 - 228474935271384*x^28 + 160873433386069*x^27 + 370623372039839*x^26 - 230144021395657*x^25 - 498856615580595*x^24 + 274166155619708*x^23 + 553790034013220*x^22 - 269823823330372*x^21 - 503089401564908*x^20 + 216992581564863*x^19 + 370319854670829*x^18 - 140486680696927*x^17 - 218142921004149*x^16 + 71749239576790*x^15 + 101233485050962*x^14 - 28097164024878*x^13 - 36271342341426*x^12 + 8090981352445*x^11 + 9766622883591*x^10 - 1598952359321*x^9 - 1901689079635*x^8 + 187537789744*x^7 + 251952870008*x^6 - 7127567376*x^5 - 20295280944*x^4 - 909912960*x^3 + 750539520*x^2 + 87091200*x time = 0.539 Factoring characteristic polynomial. [ , , , , , , , , , , , , ] time = 0.089 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^5 - 10*x^4 + 40*x^3 - 80*x^2 + 80*x - 32. Decomposing space of level 1001 and dimension 5 using T_2. (will stop at 672) Computing characteristic polynomial of T_2. x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1. Decomposing space of level 1001 and dimension 5 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^5 - 15*x^3 - 8*x^2 + 57*x + 60 time = 0 Factoring characteristic polynomial. [ , ] time = 0.01 Cutting out subspace using f(T_3), where f=x^2 - x - 5. Cutting out subspace using f(T_3), where f=x^3 + x^2 - 9*x - 12. Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x + 2. Cutting out subspace using f(T_2), where f=x^2 - 5. Cutting out subspace using f(T_2), where f=x^4 - 6*x^2 + x + 7. Cutting out subspace using f(T_2), where f=x^4 + 2*x^3 - 6*x^2 - 13*x - 5. Cutting out subspace using f(T_2), where f=x^5 - 6*x^3 + x^2 + 5*x - 2. Cutting out subspace using f(T_2), where f=x^5 + 2*x^4 - 4*x^3 - 7*x^2 + x + 2. Cutting out subspace using f(T_2), where f=x^5 + 2*x^4 - 4*x^3 - 7*x^2 + 3*x + 4. Cutting out subspace using f(T_2), where f=x^7 - 19*x^5 - x^4 + 117*x^3 + 17*x^2 - 231*x - 72. Cutting out subspace using f(T_2), where f=x^8 - 2*x^7 - 12*x^6 + 21*x^5 + 44*x^4 - 58*x^3 - 58*x^2 + 39*x + 9. Cutting out subspace using f(T_2), where f=x^11 + x^10 - 18*x^9 - 15*x^8 + 117*x^7 + 78*x^6 - 326*x^5 - 167*x^4 + 348*x^3 + 143*x^2 - 74*x - 24. Computing representation of Modular symbols space of level 1001, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on space of dimension 116. (0.029 s) Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0 s). %o x^2 - x - 5 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^3 + x^2 - 9*x - 12 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 - 5 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^4 - 6*x^2 + x + 7 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^4 + 2*x^3 - 6*x^2 - 13*x - 5 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^5 - 6*x^3 + x^2 + 5*x - 2 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^5 + 2*x^4 - 4*x^3 - 7*x^2 + x + 2 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). %o x^5 + 2*x^4 - 4*x^3 - 7*x^2 + 3*x + 4 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^7 - 19*x^5 - x^4 + 117*x^3 + 17*x^2 - 231*x - 72 p = %o, dimension = %o. 2 7 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^8 - 2*x^7 - 12*x^6 + 21*x^5 + 44*x^4 - 58*x^3 - 58*x^2 + 39*x + 9 p = %o, dimension = %o. 2 8 Computing representation of Modular symbols space of level 1001, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^11 + x^10 - 18*x^9 - 15*x^8 + 117*x^7 + 78*x^6 - 326*x^5 - 167*x^4 + 348*x^3 + 143*x^2 - 74*x - 24 p = %o, dimension = %o. 2 11 Computing cuspidal part of Full Modular symbols space of level 286, weight 2, and dimension 46 Computing cuspidal part of Modular symbols space of level 286, weight 2, and dimension 39 Computing new part of Modular symbols space of level 286, weight 2, and dimension 39. Computing 2-new part of Modular symbols space of level 286, weight 2, and dimension 39. Computing index-1 degeneracy map from level 286 to 143. (0.019 s) Computing index-2 degeneracy map from level 286 to 143. (0.019 s) Computing index-1 degeneracy map from level 143 to 286. (0.131 s) Computing index-2 degeneracy map from level 143 to 286. (0.139 s) Computing DualVectorSpace of Modular symbols space of level 286, weight 2, and dimension 39. Computing complement of Modular symbols space of level 286, weight 2, and dimension 39 Computing representation of Modular symbols space of level 286, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 46. (0 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 13 Computing T_3 on space of dimension 46. (0 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 286, weight 2, and dimension 7 Computing 11-new part of Modular symbols space of level 286, weight 2, and dimension 39. Computing space of modular symbols of level 26 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 14 relations. Form quot and then images (0.009 s) (total time to create space = 0.019 s) Computing index-1 degeneracy map from level 286 to 26. (0.009 s) Computing index-11 degeneracy map from level 286 to 26. (0.069 s) Computing index-1 degeneracy map from level 26 to 286. (0.201 s) Computing index-11 degeneracy map from level 26 to 286. (0.23 s) Computing 13-new part of Modular symbols space of level 286, weight 2, and dimension 39. Computing space of modular symbols of level 22 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.01 s) III. 3-term relations. Computing quotient by 12 relations. Form quot and then images (0.01 s) (total time to create space = 0.02 s) Computing index-1 degeneracy map from level 286 to 22. (0.011 s) Computing index-13 degeneracy map from level 286 to 22. (0.079 s) Computing index-1 degeneracy map from level 22 to 286. (0.23 s) Computing index-13 degeneracy map from level 22 to 286. (0.269 s) Decomposing space of level 286 and dimension 9 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 9. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^9 - 18*x^7 - 4*x^6 + 97*x^5 + 44*x^4 - 184*x^3 - 128*x^2 + 80*x + 64 time = 0 Factoring characteristic polynomial. [ , , , ] time = 0.01 Cutting out subspace using f(T_3), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.01 s). Charpoly = x^2 + 8*x + 16. Decomposing space of level 286 and dimension 2 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.01 s). Charpoly = x^2 - 10*x + 25. Decomposing space of level 286 and dimension 2 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 - 1 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 1. Cutting out subspace using f(T_5), where f=x + 1. Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^3 - 4*x^2. Decomposing space of level 286 and dimension 3 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^3 + 3*x^2 + 3*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^3 - 6*x^2 + 32. Decomposing space of level 286 and dimension 3 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 3. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). Computing characteristic polynomial of T_5. x^3 + 3*x^2 - x - 3 time = 0 Factoring characteristic polynomial. [ , , ] time = 0 Cutting out subspace using f(T_5), where f=x - 1. Cutting out subspace using f(T_5), where f=x + 1. Cutting out subspace using f(T_5), where f=x + 3. Cutting out subspace using f(T_3), where f=x + 2. Cutting out subspace using f(T_3), where f=x^3 - x^2 - 10*x + 8. Computing representation of Modular symbols space of level 286, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 3 2 Computing T_5 on space of dimension 46. (0.009 s) Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 286, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 286, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 286, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 286, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x + 3 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 286, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 286, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - x^2 - 10*x + 8 p = %o, dimension = %o. 3 3 Computing cuspidal part of Full Modular symbols space of level 182, weight 2, and dimension 32 Computing cuspidal part of Modular symbols space of level 182, weight 2, and dimension 25 Computing new part of Modular symbols space of level 182, weight 2, and dimension 25. Computing 2-new part of Modular symbols space of level 182, weight 2, and dimension 25. Computing index-1 degeneracy map from level 182 to 91. (0.01 s) Computing index-2 degeneracy map from level 182 to 91. (0.01 s) Computing index-1 degeneracy map from level 91 to 182. (0.101 s) Computing index-2 degeneracy map from level 91 to 182. (0.079 s) Computing DualVectorSpace of Modular symbols space of level 182, weight 2, and dimension 25. Computing complement of Modular symbols space of level 182, weight 2, and dimension 25 Computing representation of Modular symbols space of level 182, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 32. (0 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 12 Computing T_3 on space of dimension 32. (0 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 182, weight 2, and dimension 7 Computing 7-new part of Modular symbols space of level 182, weight 2, and dimension 25. Computing index-1 degeneracy map from level 182 to 26. (0.011 s) Computing index-7 degeneracy map from level 182 to 26. (0.029 s) Computing index-1 degeneracy map from level 26 to 182. (0.109 s) Computing index-7 degeneracy map from level 26 to 182. (0.171 s) Computing 13-new part of Modular symbols space of level 182, weight 2, and dimension 25. Computing space of modular symbols of level 14 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 8 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 182 to 14. (0.009 s) Computing index-13 degeneracy map from level 182 to 14. (0.049 s) Computing index-1 degeneracy map from level 14 to 182. (0.161 s) Computing index-13 degeneracy map from level 14 to 182. (0.2 s) Decomposing space of level 182 and dimension 5 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^5 - 8*x^4 + 22*x^3 - 24*x^2 + 9*x time = 0 Factoring characteristic polynomial. [ , , ] time = 0 Cutting out subspace using f(T_3), where f=x - 3. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 6*x. Decomposing space of level 182 and dimension 2 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^2 - 6*x + 9 time = 0 Factoring characteristic polynomial. [ ] time = 0.009 Cutting out subspace using f(T_3), where f=x - 3. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 12*x + 35. Decomposing space of level 182 and dimension 2 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 + 4*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x. Cutting out subspace using f(T_5), where f=x + 4. Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Charpoly = x^2 - 4*x + 3. Decomposing space of level 182 and dimension 2 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 + 6*x + 8. Decomposing space of level 182 and dimension 2 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 - 4*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 4. Cutting out subspace using f(T_5), where f=x. Cutting out subspace using f(T_3), where f=x. Computing representation of Modular symbols space of level 182, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 182, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 3 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 182, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 182, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 3 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 182, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 3 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing cuspidal part of Full Modular symbols space of level 154, weight 2, and dimension 28 Computing cuspidal part of Modular symbols space of level 154, weight 2, and dimension 21 Computing new part of Modular symbols space of level 154, weight 2, and dimension 21. Computing 2-new part of Modular symbols space of level 154, weight 2, and dimension 21. Computing index-1 degeneracy map from level 154 to 77. (0.01 s) Computing index-2 degeneracy map from level 154 to 77. (0.01 s) Computing index-1 degeneracy map from level 77 to 154. (0.101 s) Computing index-2 degeneracy map from level 77 to 154. (0.099 s) Computing DualVectorSpace of Modular symbols space of level 154, weight 2, and dimension 21. Computing complement of Modular symbols space of level 154, weight 2, and dimension 21 Computing representation of Modular symbols space of level 154, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 28. (0.01 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 10 Computing T_3 on space of dimension 28. (0 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 154, weight 2, and dimension 7 Computing 7-new part of Modular symbols space of level 154, weight 2, and dimension 21. Computing index-1 degeneracy map from level 154 to 22. (0.01 s) Computing index-7 degeneracy map from level 154 to 22. (0.03 s) Computing index-1 degeneracy map from level 22 to 154. (0.099 s) Computing index-7 degeneracy map from level 22 to 154. (0.16 s) Computing 11-new part of Modular symbols space of level 154, weight 2, and dimension 21. Computing index-1 degeneracy map from level 154 to 14. (0.009 s) Computing index-11 degeneracy map from level 154 to 14. (0.039 s) Computing index-1 degeneracy map from level 14 to 154. (0.139 s) Computing index-11 degeneracy map from level 14 to 154. (0.171 s) Decomposing space of level 154 and dimension 5 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^5 - 8*x^3 + 8*x^2 time = 0 Factoring characteristic polynomial. [ , , ] time = 0.01 Cutting out subspace using f(T_3), where f=x - 2. Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 1. Decomposing space of level 154 and dimension 2 using T_3. (will stop at 672) Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 4. Decomposing space of level 154 and dimension 2 using T_5. (will stop at 672) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 + 2*x - 8 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Cutting out subspace using f(T_5), where f=x + 4. Cutting out subspace using f(T_3), where f=x^2 + 2*x - 4. Computing representation of Modular symbols space of level 154, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 154, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 3 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 154, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 154, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 3 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^2 + 2*x - 4 p = %o, dimension = %o. 3 2 Computing cuspidal part of Full Modular symbols space of level 143, weight 2, and dimension 16 Computing cuspidal part of Modular symbols space of level 143, weight 2, and dimension 13 Computing new part of Modular symbols space of level 143, weight 2, and dimension 13. Computing 11-new part of Modular symbols space of level 143, weight 2, and dimension 13. Computing space of modular symbols of level 13 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 6 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 143 to 13. (0 s) Computing index-11 degeneracy map from level 143 to 13. (0.03 s) Computing index-1 degeneracy map from level 13 to 143. (0.04 s) Computing index-11 degeneracy map from level 13 to 143. (0.041 s) Computing DualVectorSpace of Modular symbols space of level 143, weight 2, and dimension 13. Computing complement of Modular symbols space of level 143, weight 2, and dimension 13 Computing representation of Modular symbols space of level 143, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 16. (0.009 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 143, weight 2, and dimension 3 Computing 13-new part of Modular symbols space of level 143, weight 2, and dimension 13. Computing space of modular symbols of level 11 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 143 to 11. (0 s) Computing index-13 degeneracy map from level 143 to 11. (0.029 s) Computing index-1 degeneracy map from level 11 to 143. (0.069 s) Computing index-13 degeneracy map from level 11 to 143. (0.101 s) Decomposing space of level 143 and dimension 11 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 11. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^11 - 3*x^10 - 11*x^9 + 37*x^8 + 29*x^7 - 131*x^6 - 15*x^5 + 165*x^4 + x^3 - 67*x^2 - 12*x time = 0.009 Factoring characteristic polynomial. [ , , ] time = 0 Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x^4 - 3*x^3 - x^2 + 5*x + 1. Cutting out subspace using f(T_2), where f=x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12. Computing representation of Modular symbols space of level 143, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 143 to 2002. (1.279 s) Computing index-2 degeneracy map from level 143 to 2002. (1.279 s) Computing index-7 degeneracy map from level 143 to 2002. (1.589 s) Computing index-14 degeneracy map from level 143 to 2002. (1.561 s) Computing representation of Modular symbols space of level 143, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 - 3*x^3 - x^2 + 5*x + 1 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 143, weight 2, and dimension 6. Goal dimension = 6. Computing T_2 on dual space of dimension 6. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^6 - 10*x^4 + 2*x^3 + 24*x^2 - 7*x - 12 p = %o, dimension = %o. 2 6 Computing cuspidal part of Full Modular symbols space of level 91, weight 2, and dimension 10 Computing cuspidal part of Modular symbols space of level 91, weight 2, and dimension 7 Computing new part of Modular symbols space of level 91, weight 2, and dimension 7. Computing 7-new part of Modular symbols space of level 91, weight 2, and dimension 7. Computing index-1 degeneracy map from level 91 to 13. (0.009 s) Computing index-7 degeneracy map from level 91 to 13. (0.01 s) Computing index-1 degeneracy map from level 13 to 91. (0.02 s) Computing index-7 degeneracy map from level 13 to 91. (0.03 s) Computing DualVectorSpace of Modular symbols space of level 91, weight 2, and dimension 7. Computing complement of Modular symbols space of level 91, weight 2, and dimension 7 Computing representation of Modular symbols space of level 91, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 10. (0.01 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 91, weight 2, and dimension 3 Computing 13-new part of Modular symbols space of level 91, weight 2, and dimension 7. Computing space of modular symbols of level 7 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 91 to 7. (0.01 s) Computing index-13 degeneracy map from level 91 to 7. (0.02 s) Computing index-1 degeneracy map from level 7 to 91. (0.039 s) Computing index-13 degeneracy map from level 7 to 91. (0.039 s) Decomposing space of level 91 and dimension 7 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^7 + x^6 - 8*x^5 - 8*x^4 + 16*x^3 + 12*x^2 - 8*x time = 0 Factoring characteristic polynomial. [ , , , ] time = 0.009 Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x + 2. Cutting out subspace using f(T_2), where f=x^2 - 2. Cutting out subspace using f(T_2), where f=x^3 - x^2 - 4*x + 2. Computing representation of Modular symbols space of level 91, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 91 to 2002. (1.299 s) Computing index-2 degeneracy map from level 91 to 2002. (1.421 s) Computing index-11 degeneracy map from level 91 to 2002. (1.779 s) Computing index-22 degeneracy map from level 91 to 2002. (1.599 s) Computing representation of Modular symbols space of level 91, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 91, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - 2 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 91, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - x^2 - 4*x + 2 p = %o, dimension = %o. 2 3 Computing cuspidal part of Full Modular symbols space of level 77, weight 2, and dimension 10 Computing cuspidal part of Modular symbols space of level 77, weight 2, and dimension 7 Computing new part of Modular symbols space of level 77, weight 2, and dimension 7. Computing 7-new part of Modular symbols space of level 77, weight 2, and dimension 7. Computing index-1 degeneracy map from level 77 to 11. (0 s) Computing index-7 degeneracy map from level 77 to 11. (0.019 s) Computing index-1 degeneracy map from level 11 to 77. (0.049 s) Computing index-7 degeneracy map from level 11 to 77. (0.06 s) Computing DualVectorSpace of Modular symbols space of level 77, weight 2, and dimension 7. Computing complement of Modular symbols space of level 77, weight 2, and dimension 7 Computing representation of Modular symbols space of level 77, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 10. (0 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 77, weight 2, and dimension 3 Computing 11-new part of Modular symbols space of level 77, weight 2, and dimension 7. Computing index-1 degeneracy map from level 77 to 7. (0 s) Computing index-11 degeneracy map from level 77 to 7. (0.01 s) Computing index-1 degeneracy map from level 7 to 77. (0.041 s) Computing index-11 degeneracy map from level 7 to 77. (0.049 s) Decomposing space of level 77 and dimension 5 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^5 - x^4 - 5*x^3 + 5*x^2 time = 0 Factoring characteristic polynomial. [ , , ] time = 0 Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^2. Decomposing space of level 77 and dimension 2 using T_2. (will stop at 672) Computing characteristic polynomial of T_2. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^2. Decomposing space of level 77 and dimension 2 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^2 + 2*x - 3 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x - 1. Cutting out subspace using f(T_3), where f=x + 3. Cutting out subspace using f(T_2), where f=x^2 - 5. Computing representation of Modular symbols space of level 77, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 77 to 2002. (1.609 s) Computing index-2 degeneracy map from level 77 to 2002. (1.701 s) Computing index-13 degeneracy map from level 77 to 2002. (2.04 s) Computing index-26 degeneracy map from level 77 to 2002. (1.899 s) Computing representation of Modular symbols space of level 77, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 2 Computing T_3 on space of dimension 10. (0 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 77, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 77, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - 5 p = %o, dimension = %o. 2 2 Computing cuspidal part of Full Modular symbols space of level 26, weight 2, and dimension 5 Computing cuspidal part of Modular symbols space of level 26, weight 2, and dimension 2 Computing new part of Modular symbols space of level 26, weight 2, and dimension 2. Computing 2-new part of Modular symbols space of level 26, weight 2, and dimension 2. Computing index-1 degeneracy map from level 26 to 13. (0 s) Computing index-2 degeneracy map from level 26 to 13. (0.01 s) Computing index-1 degeneracy map from level 13 to 26. (0.01 s) Computing index-2 degeneracy map from level 13 to 26. (0.01 s) Computing DualVectorSpace of Modular symbols space of level 26, weight 2, and dimension 2. Goal dimension = 2. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 2. Computing T_2 on space of dimension 5. (0 s) (0 s) %o x^2 - 1 p = 2, dimension = 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing T_3 on space of dimension 2. Computing T_3 on space of dimension 5. (0 s) (0 s) %o x^2 + 2*x - 3 p = 3, dimension = 2. Computing 13-new part of Modular symbols space of level 26, weight 2, and dimension 2. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 26 to 2. (0.01 s) Computing index-13 degeneracy map from level 26 to 2. (0.01 s) Computing index-1 degeneracy map from level 2 to 26. (0.04 s) Computing index-13 degeneracy map from level 2 to 26. (0.041 s) Decomposing space of level 26 and dimension 2 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^2 + 2*x - 3 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x - 1. Cutting out subspace using f(T_3), where f=x + 3. Computing representation of Modular symbols space of level 26, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 26 to 2002. (2.089 s) Computing index-7 degeneracy map from level 26 to 2002. (2.361 s) Computing index-11 degeneracy map from level 26 to 2002. (2.379 s) Computing index-77 degeneracy map from level 26 to 2002. (2.221 s) Computing representation of Modular symbols space of level 26, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing cuspidal part of Full Modular symbols space of level 22, weight 2, and dimension 5 Computing cuspidal part of Modular symbols space of level 22, weight 2, and dimension 2 Computing new part of Modular symbols space of level 22, weight 2, and dimension 2. Computing 2-new part of Modular symbols space of level 22, weight 2, and dimension 2. Computing index-1 degeneracy map from level 22 to 11. (0 s) Computing index-2 degeneracy map from level 22 to 11. (0.01 s) Computing index-1 degeneracy map from level 11 to 22. (0.02 s) Computing index-2 degeneracy map from level 11 to 22. (0.021 s) Computing DualVectorSpace of Modular symbols space of level 22, weight 2, and dimension 2. Goal dimension = 2. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 2. Computing T_2 on space of dimension 5. (0 s) (0 s) %o x^2 + 2*x + 2 p = 2, dimension = 2. Computing 11-new part of Modular symbols space of level 22, weight 2, and dimension 2. Computing index-1 degeneracy map from level 22 to 2. (0 s) Computing index-11 degeneracy map from level 22 to 2. (0.019 s) Computing index-1 degeneracy map from level 2 to 22. (0.029 s) Computing index-11 degeneracy map from level 2 to 22. (0.039 s) Computing cuspidal part of Full Modular symbols space of level 14, weight 2, and dimension 4 Computing cuspidal part of Modular symbols space of level 14, weight 2, and dimension 1 Computing new part of Modular symbols space of level 14, weight 2, and dimension 1. Computing 2-new part of Modular symbols space of level 14, weight 2, and dimension 1. Computing index-1 degeneracy map from level 14 to 7. (0 s) Computing index-2 degeneracy map from level 14 to 7. (0 s) Computing index-1 degeneracy map from level 7 to 14. (0.009 s) Computing index-2 degeneracy map from level 7 to 14. (0.01 s) Computing DualVectorSpace of Modular symbols space of level 14, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 4. (0 s) (0 s) %o x + 1 p = 2, dimension = 1. Computing 7-new part of Modular symbols space of level 14, weight 2, and dimension 1. Computing index-1 degeneracy map from level 14 to 2. (0.01 s) Computing index-7 degeneracy map from level 14 to 2. (0 s) Computing index-1 degeneracy map from level 2 to 14. (0.02 s) Computing index-7 degeneracy map from level 2 to 14. (0.03 s) Decomposing space of level 14 and dimension 1 using T_3. (will stop at 672) Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x + 2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 2. Computing index-1 degeneracy map from level 14 to 2002. (3.401 s) Computing index-11 degeneracy map from level 14 to 2002. (3.559 s) Computing index-13 degeneracy map from level 14 to 2002. (3.76 s) Computing index-143 degeneracy map from level 14 to 2002. (3.861 s) Computing cuspidal part of Full Modular symbols space of level 11, weight 2, and dimension 2 Computing cuspidal part of Modular symbols space of level 11, weight 2, and dimension 1 Computing new part of Modular symbols space of level 11, weight 2, and dimension 1. Computing 11-new part of Modular symbols space of level 11, weight 2, and dimension 1. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 11 and dimension 1 using T_2. (will stop at 672) Computing T_2 on dual space of dimension 1. Computing DualVectorSpace of Modular symbols space of level 11, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 2. (0.01 s) (0.01 s) %o x + 2 p = 2, dimension = 1. T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x + 2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 2. Computing index-1 degeneracy map from level 11 to 2002. (5.28 s) Computing index-2 degeneracy map from level 11 to 2002. (4.071 s) Computing index-7 degeneracy map from level 11 to 2002. (3.939 s) Computing index-13 degeneracy map from level 11 to 2002. (4.29 s) Computing index-14 degeneracy map from level 11 to 2002. (3.881 s) Computing index-26 degeneracy map from level 11 to 2002. (4.64 s) Computing index-91 degeneracy map from level 11 to 2002. (3.789 s) Computing index-182 degeneracy map from level 11 to 2002. (4.319 s) Sorting ... 11.931 seconds. Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.021 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.011 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.011 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.019 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.019 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.019 s). T_29 sparse... (0.011 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.011 s). T_13 sparse... (0.019 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 3. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 3. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 3. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 3. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 3. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 3. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 3. T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 3. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 3. T_37 sparse... (0.009 s). T_37 sparse... (0.021 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 3. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 3. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 3. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 3. T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 3. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 3. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). Computing T_29 on dual space of dimension 3. T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 3. T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 3. T_37 sparse... (0.011 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 3. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 3. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 3. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 3. T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 3. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 3. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 3. T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 3. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 3. T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 4. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 4. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 4. T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 4. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.02 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 4. T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 4. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 4. T_29 sparse... (0.011 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 4. T_31 sparse... (0.009 s). T_31 sparse... (0.02 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 4. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 4. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 4. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 4. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 4. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.021 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 4. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 4. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). Computing T_29 on dual space of dimension 4. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 4. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.011 s). Computing T_37 on dual space of dimension 4. T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 5. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 5. T_11 sparse... (0.009 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 5. T_13 sparse... (0.01 s). T_13 sparse... (0.019 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 5. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 5. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.019 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 5. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 5. T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 5. T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.021 s). T_31 sparse... (0.009 s). T_31 sparse... (0.011 s). Computing T_37 on dual space of dimension 5. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 5. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 5. T_11 sparse... (0.011 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 5. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.02 s). Computing T_17 on dual space of dimension 5. T_17 sparse... (0.009 s). T_17 sparse... (0.02 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 5. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 5. T_23 sparse... (0.009 s). T_23 sparse... (0.02 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 5. T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 5. T_31 sparse... (0.019 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.021 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 5. T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 5. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 5. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 5. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 5. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 5. T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.02 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 5. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 5. T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). Computing T_31 on dual space of dimension 5. T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 5. T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 5. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 5. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 5. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 5. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 5. T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 5. T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 5. T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 5. T_31 sparse... (0.009 s). T_31 sparse... (0.011 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 5. T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 5. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 5. T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 5. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 5. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 5. T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 5. T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 5. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.019 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 5. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.019 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 5. T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 5. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 6. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 6. T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 6. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 6. T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.02 s). T_13 sparse... (0.01 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 6. T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). T_17 sparse... (0.02 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 6. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 6. T_23 sparse... (0.009 s). T_23 sparse... (0.02 s). T_23 sparse... (0.01 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 6. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.009 s). T_29 sparse... (0.02 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 6. T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.019 s). Computing T_37 on dual space of dimension 6. T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.019 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.02 s). Computing q-expansion. T_2 sparse... (0.01 s). T_3 sparse... (0.01 s). T_5 sparse... (0.009 s). T_7 sparse... (0.011 s). T_11 sparse... (0.009 s). T_13 sparse... (0.01 s). T_17 sparse... (0.009 s). T_19 sparse... (0.01 s). T_23 sparse... (0.009 s). T_29 sparse... (0.01 s). T_31 sparse... (0.009 s). T_37 sparse... (0.009 s). (0.161 s) Computing q-expansion. (0.01 s) Computing q-expansion. (0.01 s) Computing q-expansion. (0.029 s) Computing q-expansion. (0.041 s) Computing q-expansion. T_2 sparse... (0.01 s). T_3 sparse... (0.009 s). T_5 sparse... (0.01 s). T_7 sparse... (0.009 s). T_11 sparse... (0.01 s). T_13 sparse... (0.009 s). T_17 sparse... (0.01 s). T_19 sparse... (0.019 s). T_23 sparse... (0.009 s). T_29 sparse... (0.01 s). T_31 sparse... (0.009 s). T_37 sparse... (0.009 s). (0.18 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.04 s) Computing q-expansion. (0.041 s) Computing q-expansion. (0.04 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.05 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.07 s) Computing q-expansion. (0.05 s) Computing q-expansion. (0.049 s) Computing character group of torus of J_0(2*1001)/F_2. 152.67 seconds. Computing T_2 on space of dimension 1. (0.02 s) Computing T_3 on space of dimension 1. (0.019 s) Computing T_5 on space of dimension 1. (0.019 s) Computing T_7 on space of dimension 1. (0.019 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing character group of torus of J_0(7*286)/F_7. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 2161008971 Time to this point: 2568.83 Segmentation fault >> -2250.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2002, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 2569.659 seconds Magma V2.7-1 Mon Jan 29 2001 03:38:36 on modular [Seed = 1477871516] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2003 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.62 s) III. 3-term relations. Computing quotient by 668 relations. Form quot and then images (0.369 s) (total time to create space = 1.019 s) Computing cuspidal part of Full Modular symbols space of level 2003, weight 2, and dimension 168 Computing new part of Modular symbols space of level 2003, weight 2, and dimension 167. Computing 2003-new part of Modular symbols space of level 2003, weight 2, and dimension 167. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Finding newform decomposition of Modular symbols space of level 2003, weight 2, and dimension 167. Computing 2003-new part of Modular symbols space of level 2003, weight 2, and dimension 167. Computing cuspidal part of Modular symbols space of level 2003, weight 2, and dimension 167 Decomposing space of level 2003 and dimension 167 using T_2. (will stop at 334) Computing T_2 on dual space of dimension 167. Computing DualVectorSpace of Modular symbols space of level 2003, weight 2, and dimension 167. Computing complement of Modular symbols space of level 2003, weight 2, and dimension 167 Computing representation of Modular symbols space of level 2003, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 168. (0.341 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 2003, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^167 + 2*x^166 - 247*x^165 - 490*x^164 + 29896*x^163 + 58812*x^162 - 2363564*x^161 - 4609512*x^160 + 137274375*x^159 + 265331640*x^158 - 6245713959*x^157 - 11960988836*x^156 + 231816644625*x^155 + 439728449842*x^154 - 7217365374539*x^153 - 13556235383732*x^152 + 192354682069230*x^151 + 357639113118934*x^150 - 4456727920963256*x^149 - 8199688410326626*x^148 + 90859385575645403*x^147 + 165364696799564556*x^146 - 1645813215577160247*x^145 - 2962058669999471906*x^144 + 26699322913619547157*x^143 + 47500394526776367966*x^142 - 390479944417033726572*x^141 - 686465321019527565786*x^140 + 5177167718128201215441*x^139 + 8990197040019393483634*x^138 - 62522490129554790405208*x^137 - 107201183565735063458704*x^136 + 690548870752271215133486*x^135 + 1168606191850415199013632*x^134 - 6999876658109585586497648*x^133 - 11686741572769152301284828*x^132 + 65320278331282908826216545*x^131 + 107545878295870234493664652*x^130 - 562629725229617013355584058*x^129 - 913101160583810386934913994*x^128 + 4483590811748843110592361435*x^127 + 7169265239935242874171593662*x^126 - 33124228888919876687549726911*x^125 - 52160635356190624813502794882*x^124 + 227280567163377852775197019155*x^123 + 352287742929485300144672094058*x^122 - 1450645564787739037416980888683*x^121 - 2212166899642957610406504094804*x^120 + 8624719860446342508009448138533*x^119 + 12933002173525428077177305317264*x^118 - 47823460997352317098617512099628*x^117 - 70479443808897197543830236829718*x^116 + 247576817441326315164635316065526*x^115 + 358393760452261530978022848868232*x^114 - 1197710564864966575206807050038409*x^113 - 1702101237329601037416872764201600*x^112 + 5418902300438477540779158468682949*x^111 + 7555681216601951222545162210128410*x^110 - 22944681482298474039175901256957272*x^109 - 31369680855784828651376107278873232*x^108 + 90972614915311351407457878706587731*x^107 + 121879905494922606292104188751420820*x^106 - 337909224827453781239341467424315873*x^105 - 443335423231401847721800767094684702*x^104 + 1176282855128089750722105790534525307*x^103 + 1510295584460868888063593897502739220*x^102 - 3838562001657172503367136292255570325*x^101 - 4819830956303858516433456995209482180*x^100 + 11745084390474544369496917945630448090*x^99 + 14411698628218571097249698771462049280*x^98 - 33699602246894442922025563875167723618*x^97 - 40378360737331421893713650185565271154*x^96 + 90675619528678594373437752403333719450*x^95 + 106006756493793762679855172040664038134*x^94 - 228789603650360544592237862690705673827*x^93 - 260757226095972187800626839049778646582*x^92 + 541268142245974993102189342515927143634*x^91 + 600882605886059068796789751475087345368*x^90 - 1200432039442475573252424257807865511377*x^89 - 1296857186447431572900897192283658672090*x^88 + 2495160667805681736533241412537918992435*x^87 + 2620649663501891619389361832965588887924*x^86 - 4859042181449535445581066125670498282736*x^85 - 4956455636266348317008399651689919662140*x^84 + 8861716087682415170680800403028148168127*x^83 + 8769518215092551709835345362086660873152*x^82 - 15128362141640575039470818251937201510406*x^81 - 14507223362180113633999146293761307770450*x^80 + 24161975639441132394347522886355988124875*x^79 + 22424499465605866516447487406750692537694*x^78 - 36079946389693688665048797896137633231211*x^77 - 32365311991351858453770584765789368032662*x^76 + 50336696970194420397896875455838718066938*x^75 + 43581827016638782524568256011308830084758*x^74 - 65561108058257261554349143569534529485461*x^73 - 54702752660768461706428648212938904516588*x^72 + 79647367186810161053745524342227267700832*x^71 + 63937827078212978705886534933553931057150*x^70 - 90165992425908165848172424765933549716705*x^69 - 69514123289672350444682413244315031062606*x^68 + 95017319287576711424582981400969151125233*x^67 + 70214675363832407477472482579442780601924*x^66 - 93100368210445139264912282214678324499501*x^65 - 65802682679777040517896924917618693792532*x^64 + 84711693237797699693331309733274557135260*x^63 + 57132749562720332758603084429996307090164*x^62 - 71480068598575846631714425222281345177269*x^61 - 45883458063655405032869371781146968320164*x^60 + 55850920649796650967861230051542321739216*x^59 + 34024603359221846789239819812446620619756*x^58 - 40343830352676125827023892602760431824095*x^57 - 23251875033348723219741908959751597765006*x^56 + 26894370163477487485959492726816219813801*x^55 + 14612686110699011715433431274810409480762*x^54 - 16513972329514335345463495772847876161431*x^53 - 8425492548734837183619099228205360644060*x^52 + 9320549763419485401023894098126133332663*x^51 + 4445636411495796785822510746951241905786*x^50 - 4824388965414560018598556049831954019080*x^49 - 2140448990246854108968123632734932515398*x^48 + 2284400511367091031419549330822743552476*x^47 + 937402670204861714576208145871921682152*x^46 - 986836848673659031525748996016666748082*x^45 - 372091878850633346652011356614912896114*x^44 + 387755051803103542447453200804145470711*x^43 + 133330993628270016781749874669219597360*x^42 - 138124116384101831371756148888354178173*x^41 - 42932069625832327936152021023342780396*x^40 + 44441371000733493632222877432098438043*x^39 + 12357038518875158378634630867121089878*x^38 - 12862867176245312932822302005924791974*x^37 - 3159769485325065498161413267706401332*x^36 + 3333785889222671028460725488604314657*x^35 + 712556838417096728185283204802043830*x^34 - 769764993612442161245936409470349254*x^33 - 140446320262103398821047149165564868*x^32 + 157426521917321738425065721055654682*x^31 + 23921240802683240721514876892571792*x^30 - 28328633065789367453185576877630075*x^29 - 3467560231135625503340158831999868*x^28 + 4451498049756155014991238118584807*x^27 + 418450394568161391013608181960678*x^26 - 605487991748090119016494683299926*x^25 - 40539184582989009794678175790846*x^24 + 70561251479863297738685289686899*x^23 + 2927522576610756059487882691834*x^22 - 6960220529302736142947458535880*x^21 - 124399921070461125790536176114*x^20 + 572771697065208456740613103463*x^19 - 2055905946679331147227141832*x^18 - 38638517802014524331872884645*x^17 + 870324900342628498961642804*x^16 + 2091149532885649764685308286*x^15 - 80414421134652034777704174*x^14 - 88396591621743304859580332*x^13 + 4485258562104205718697292*x^12 + 2821577344563746643582611*x^11 - 165130753667024140954650*x^10 - 65124949938821219473087*x^9 + 3955917157781084527494*x^8 + 1026399116350376936176*x^7 - 57939648851720200472*x^6 - 10164577059374942288*x^5 + 467009163915827072*x^4 + 54652504289772480*x^3 - 1827479341609984*x^2 - 112984790941952*x + 3075789763072 time = 2.089 Factoring characteristic polynomial. [ , ] time = 0.951 Cutting out subspace using f(T_2), where f=x^75 + 7*x^74 - 82*x^73 - 672*x^72 + 3020*x^71 + 30684*x^70 - 63461*x^69 - 886987*x^68 + 743018*x^67 + 18227564*x^66 - 1494976*x^65 - 283462632*x^64 - 124626517*x^63 + 3467270610*x^62 + 2882596337*x^61 - 34228227304*x^60 - 39229527083*x^59 + 277634632142*x^58 + 392720308842*x^57 - 1874093825934*x^56 - 3104453874588*x^55 + 10623307225299*x^54 + 20044036978691*x^53 - 50880974009883*x^52 - 107767519915809*x^51 + 206685906714343*x^50 + 488410086636909*x^49 - 713170455367194*x^48 - 1880819043931880*x^47 + 2088643056339331*x^46 + 6186561887336640*x^45 - 5173418038625173*x^44 - 17438180182877985*x^43 + 10756973693854742*x^42 + 42192657455048922*x^41 - 18514998117852705*x^40 - 87665334329266511*x^39 + 25670539545276089*x^38 + 156296081032420366*x^37 - 26937394559714702*x^36 - 238676559255017036*x^35 + 17356013571004927*x^34 + 311300074142965589*x^33 + 2940951894168932*x^32 - 345443959802207517*x^31 - 26454029084644834*x^30 + 324541786392994789*x^29 + 42317311628250481*x^28 - 256595641182492765*x^27 - 44138428131841911*x^26 + 169512667731102734*x^25 + 34260250452501522*x^24 - 92784886311341477*x^23 - 20499257590873376*x^22 + 41670111659051174*x^21 + 9518907650489371*x^20 - 15180937062048298*x^19 - 3406741747047157*x^18 + 4426571421565311*x^17 + 924106278663941*x^16 - 1016314816052964*x^15 - 184937895225931*x^14 + 179899438975346*x^13 + 26207210551528*x^12 - 23845093542151*x^11 - 2463228606471*x^10 + 2266597081041*x^9 + 136531870916*x^8 - 144531481075*x^7 - 3437549788*x^6 + 5561582016*x^5 + 22068952*x^4 - 109480514*x^3 - 1834938*x^2 + 942003*x + 46429. Cutting out subspace using f(T_2), where f=x^92 - 5*x^91 - 130*x^90 + 682*x^89 + 8082*x^88 - 44782*x^87 - 319581*x^86 + 1885497*x^85 + 9014739*x^84 - 57206041*x^83 - 192741510*x^82 + 1332584672*x^81 + 3236901499*x^80 - 24797199148*x^79 - 43599529474*x^78 + 378670886883*x^77 + 475511135377*x^76 - 4837938741164*x^75 - 4186363753716*x^74 + 52461247439730*x^73 + 29024265406911*x^72 - 488156014981249*x^71 - 145489800221182*x^70 + 3931108386203149*x^69 + 335442132304988*x^68 - 27580435170197431*x^67 + 2615779262624587*x^66 + 169468284822120416*x^65 - 42303795329210362*x^64 - 915695369282580630*x^63 + 351906124576179451*x^62 + 4364693008077366030*x^61 - 2194918319102602882*x^60 - 18395669231773170827*x^59 + 11193149953851595471*x^58 + 68668236058933164041*x^57 - 48311303100162239759*x^56 - 227261938789118467360*x^55 + 179572229125763123464*x^54 + 667168874253546905329*x^53 - 580445133097035249545*x^52 - 1737244792162116050315*x^51 + 1641042255115003606245*x^50 + 4010125933335239589375*x^49 - 4071740972663481018832*x^48 - 8197112285297078602447*x^47 + 8882044233029556292879*x^46 + 14814142866917256362177*x^45 - 17044329942656457836859*x^44 - 23619539508731337255704*x^43 + 28763276183351130426343*x^42 + 33132147040966459342168*x^41 - 42638233605784461743644*x^40 - 40749180457835466983506*x^39 + 55418838267392892587515*x^38 + 43756375233481681519546*x^37 - 62994480461368658549123*x^36 - 40809322699512902079456*x^35 + 62418621561375960022495*x^34 + 32846130613217729619319*x^33 - 53696344737109498557249*x^32 - 22631836358959624112699*x^31 + 39910572883293182306790*x^30 + 13212010946450139593199*x^29 - 25481986399169557646127*x^28 - 6444680495870266049928*x^27 + 13880385888765294045530*x^26 + 2575020531332701771659*x^25 - 6398196072684999122525*x^24 - 816469367957552044593*x^23 + 2471670958859116935930*x^22 + 193332575218202282842*x^21 - 790951817592281071785*x^20 - 28940521811253376895*x^19 + 206733940085889804530*x^18 + 442911982025386303*x^17 - 43374843544192614777*x^16 + 1108612586177942822*x^15 + 7147457453949176670*x^14 - 334903080748409380*x^13 - 899243646066349094*x^12 + 55804867431103334*x^11 + 83142320434386965*x^10 - 5947135714080277*x^9 - 5347249903916970*x^8 + 405653531938888*x^7 + 219391463729464*x^6 - 16736070210512*x^5 - 4901309245632*x^4 + 374472227264*x^3 + 39901422848*x^2 - 3777592064*x + 66247168. Computing representation of Modular symbols space of level 2003, weight 2, and dimension 75. Goal dimension = 75. Computing T_2 on dual space of dimension 75. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^75 + 7*x^74 - 82*x^73 - 672*x^72 + 3020*x^71 + 30684*x^70 - 63461*x^69 - 886987*x^68 + 743018*x^67 + 18227564*x^66 - 1494976*x^65 - 283462632*x^64 - 124626517*x^63 + 3467270610*x^62 + 2882596337*x^61 - 34228227304*x^60 - 39229527083*x^59 + 277634632142*x^58 + 392720308842*x^57 - 1874093825934*x^56 - 3104453874588*x^55 + 10623307225299*x^54 + 20044036978691*x^53 - 50880974009883*x^52 - 107767519915809*x^51 + 206685906714343*x^50 + 488410086636909*x^49 - 713170455367194*x^48 - 1880819043931880*x^47 + 2088643056339331*x^46 + 6186561887336640*x^45 - 5173418038625173*x^44 - 17438180182877985*x^43 + 10756973693854742*x^42 + 42192657455048922*x^41 - 18514998117852705*x^40 - 87665334329266511*x^39 + 25670539545276089*x^38 + 156296081032420366*x^37 - 26937394559714702*x^36 - 238676559255017036*x^35 + 17356013571004927*x^34 + 311300074142965589*x^33 + 2940951894168932*x^32 - 345443959802207517*x^31 - 26454029084644834*x^30 + 324541786392994789*x^29 + 42317311628250481*x^28 - 256595641182492765*x^27 - 44138428131841911*x^26 + 169512667731102734*x^25 + 34260250452501522*x^24 - 92784886311341477*x^23 - 20499257590873376*x^22 + 41670111659051174*x^21 + 9518907650489371*x^20 - 15180937062048298*x^19 - 3406741747047157*x^18 + 4426571421565311*x^17 + 924106278663941*x^16 - 1016314816052964*x^15 - 184937895225931*x^14 + 179899438975346*x^13 + 26207210551528*x^12 - 23845093542151*x^11 - 2463228606471*x^10 + 2266597081041*x^9 + 136531870916*x^8 - 144531481075*x^7 - 3437549788*x^6 + 5561582016*x^5 + 22068952*x^4 - 109480514*x^3 - 1834938*x^2 + 942003*x + 46429 p = %o, dimension = %o. 2 75 Computing representation of Modular symbols space of level 2003, weight 2, and dimension 92. Computing complement of Modular symbols space of level 2003, weight 2, and dimension 92 Computing DualVectorSpace of Modular symbols space of level 2003, weight 2, and dimension 76. Goal dimension = 76. T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_2 on space of dimension 76. (0.28 s) %o x^76 + 4*x^75 - 103*x^74 - 426*x^73 + 5036*x^72 + 21624*x^71 - 155513*x^70 - 696604*x^69 + 3403979*x^68 + 15998510*x^67 - 56177668*x^66 - 278977704*x^65 + 725761379*x^64 + 3841150161*x^63 - 7519215493*x^62 - 42876016315*x^61 + 63455154829*x^60 + 395323213391*x^59 - 440183587584*x^58 - 3052254752460*x^57 + 2517827603214*x^56 + 19936668849063*x^55 - 11825884697206*x^54 - 111013084945956*x^53 + 44875402113840*x^52 + 529988466461770*x^51 - 131647633506120*x^50 - 2178400715277921*x^49 + 258692322169702*x^48 + 7731100188134971*x^47 - 79367281681353*x^46 - 23733103700635093*x^45 - 1917926067002466*x^44 + 63071514242488697*x^43 + 9921736373484696*x^42 - 145092970482999471*x^41 - 32120339975708396*x^40 + 288666542533075622*x^39 + 79284462396592099*x^38 - 495825637656975800*x^37 - 157864375575872930*x^36 + 733385691336056035*x^35 + 259232033429950808*x^34 - 930959270534727835*x^33 - 354266815484714313*x^32 + 1009877850321977717*x^31 + 403903873646929291*x^30 - 931308047550733886*x^29 - 383547576067244208*x^28 + 725648495415636384*x^27 + 301927952126628467*x^26 - 474277752740806680*x^25 - 195565637668846043*x^24 + 257855401343151055*x^23 + 103167884431671302*x^22 - 115491427326664151*x^21 - 43737660013516411*x^20 + 42136069439097737*x^19 + 14646796662706782*x^18 - 12355607986031992*x^17 - 3788633652044787*x^16 + 2864006552932961*x^15 + 734713124653139*x^14 - 513491106374510*x^13 - 102466725196735*x^12 + 69072052019982*x^11 + 9656282900454*x^10 - 6663259372207*x^9 - 554127093823*x^8 + 430156893437*x^7 + 15874231380*x^6 - 16662677096*x^5 - 175687370*x^4 + 326606604*x^3 + 6446817*x^2 - 2779580*x - 139287 p = 2, dimension = 76. Computing complement of Modular symbols space of level 2003, weight 2, and dimension 76 Sorting ... 0 seconds. Computing T_3 on dual space of dimension 75. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 75. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 75. T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 75. T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 75. T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 75. T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). Computing T_19 on dual space of dimension 75. T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 75. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 75. T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). Computing T_31 on dual space of dimension 75. T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 75. T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). Computing T_2 on dual space of dimension 92. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 92. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 92. T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 92. T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 92. T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 92. T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 92. T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.01 s). T_17 sparse... (0 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). T_17 sparse... (0.009 s). T_17 sparse... (0 s). Computing T_19 on dual space of dimension 92. T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0.011 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 92. T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 92. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 92. T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0 s). T_31 sparse... (0 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 92. T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing q-expansion. T_2 sparse... (0 s). T_3 sparse... (0.01 s). T_5 sparse... (0 s). T_7 sparse... (0.011 s). T_11 sparse... (0 s). T_13 sparse... (0 s). T_17 sparse... (0.009 s). T_19 sparse... (0 s). T_23 sparse... (0.009 s). T_29 sparse... (0.009 s). T_31 sparse... (0 s). T_37 sparse... (0.009 s). (7.591 s) Computing q-expansion. (16.191 s) Computing T_2 on space of dimension 75. (0.311 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 92. (0.451 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_3 on space of dimension 75. Computing T_3 on space of dimension 168. (0.051 s) (0.461 s) Computing T_5 on space of dimension 75. Computing T_5 on space of dimension 168. (0.059 s) (0.45 s) Computing T_7 on space of dimension 75. Computing T_7 on space of dimension 168. (0.081 s) (0.561 s) Computing T_11 on space of dimension 75. Computing T_11 on space of dimension 168. (0.109 s) (0.689 s) Computing T_13 on space of dimension 75. Computing T_13 on space of dimension 168. (0.129 s) (0.679 s) Computing T_17 on space of dimension 75. Computing T_17 on space of dimension 168. (0.159 s) (0.74 s) Computing T_19 on space of dimension 75. Computing T_19 on space of dimension 168. (0.19 s) (0.789 s) Computing T_23 on space of dimension 75. Computing T_23 on space of dimension 168. (0.22 s) (0.849 s) Computing T_29 on space of dimension 75. Computing T_29 on space of dimension 168. (0.269 s) (0.889 s) Computing T_31 on space of dimension 75. Computing T_31 on space of dimension 168. (0.299 s) (0.929 s) Computing T_37 on space of dimension 75. Computing T_37 on space of dimension 168. (0.339 s) (0.959 s) Computing T_3 on space of dimension 92. (0.509 s) Computing T_5 on space of dimension 92. (0.549 s) Computing T_7 on space of dimension 92. (0.68 s) Computing T_11 on space of dimension 92. (0.75 s) Computing T_13 on space of dimension 92. (0.76 s) Computing T_17 on space of dimension 92. (0.789 s) Computing T_19 on space of dimension 92. (0.8 s) Computing T_23 on space of dimension 92. (0.829 s) Computing T_29 on space of dimension 92. (0.831 s) Computing T_31 on space of dimension 92. (0.83 s) Computing T_37 on space of dimension 92. (0.839 s) Computing T_1 on space of dimension 168. (0 s) T_2 sparse... (0.009 s). T_3 sparse... (0 s). Computing T_4 on space of dimension 168. (0.029 s) T_5 sparse... (0 s). Computing T_6 on space of dimension 168. (0.019 s) T_7 sparse... (0 s). Computing T_8 on space of dimension 168. (0.029 s) Computing T_9 on space of dimension 168. (0.029 s) Computing T_10 on space of dimension 168. (0.01 s) T_11 sparse... (0.01 s). Computing T_12 on space of dimension 168. (0.02 s) T_13 sparse... (0 s). Computing T_14 on space of dimension 168. (0.02 s) Computing T_15 on space of dimension 168. (0.021 s) Computing T_16 on space of dimension 168. (0.029 s) T_17 sparse... (0.009 s). Computing T_18 on space of dimension 168. (0.019 s) T_19 sparse... (0 s). Computing T_20 on space of dimension 168. (0.029 s) Computing T_21 on space of dimension 168. (0.029 s) Computing T_22 on space of dimension 168. (0.02 s) T_23 sparse... (0.01 s). Computing T_24 on space of dimension 168. (0.03 s) Computing T_25 on space of dimension 168. (0.031 s) Computing T_26 on space of dimension 168. (0.019 s) Computing T_27 on space of dimension 168. (0.029 s) Computing T_28 on space of dimension 168. (0.029 s) T_29 sparse... (0.009 s). Computing T_30 on space of dimension 168. (0.019 s) T_31 sparse... (0 s). Computing T_32 on space of dimension 168. (0.04 s) Computing T_33 on space of dimension 168. (0.03 s) Computing T_34 on space of dimension 168. (0.031 s) Computing T_35 on space of dimension 168. (0.029 s) Computing T_36 on space of dimension 168. (0.029 s) T_37 sparse... (0 s). Computing T_38 on space of dimension 168. (0.019 s) Computing T_39 on space of dimension 168. (0.029 s) Computing T_40 on space of dimension 168. (0.03 s) T_41 sparse... (0.01 s). Computing T_42 on space of dimension 168. (0.02 s) T_43 sparse... (0.01 s). Computing T_44 on space of dimension 168. (0.031 s) Computing T_45 on space of dimension 168. (0.029 s) Computing T_46 on space of dimension 168. (0.019 s) T_47 sparse... (0.009 s). Computing T_48 on space of dimension 168. (0.039 s) Computing T_49 on space of dimension 168. (0.04 s) Computing T_50 on space of dimension 168. (0.02 s) Computing T_51 on space of dimension 168. (0.02 s) Computing T_52 on space of dimension 168. (0.029 s) T_53 sparse... (0.019 s). Computing T_54 on space of dimension 168. (0.019 s) Computing T_55 on space of dimension 168. (0.019 s) Computing T_56 on space of dimension 168. (0.039 s) Computing T_57 on space of dimension 168. (0.03 s) Computing T_58 on space of dimension 168. (0.02 s) T_59 sparse... (0.01 s). Computing T_60 on space of dimension 168. (0.031 s) T_61 sparse... (0.009 s). Computing T_62 on space of dimension 168. (0.019 s) Computing T_63 on space of dimension 168. (0.029 s) Computing T_64 on space of dimension 168. (0.029 s) Computing T_65 on space of dimension 168. (0.02 s) Computing T_66 on space of dimension 168. (0.02 s) T_67 sparse... (0.02 s). Computing T_68 on space of dimension 168. (0.031 s) Computing T_69 on space of dimension 168. (0.029 s) Computing T_70 on space of dimension 168. (0.019 s) T_71 sparse... (0.009 s). Computing T_72 on space of dimension 168. (0.039 s) T_73 sparse... (0.01 s). Computing T_74 on space of dimension 168. (0.02 s) Computing T_75 on space of dimension 168. (0.02 s) Computing T_76 on space of dimension 168. (0.031 s) Computing T_77 on space of dimension 168. (0.039 s) Computing T_78 on space of dimension 168. (0.019 s) T_79 sparse... (0.019 s). Computing T_80 on space of dimension 168. (0.039 s) Computing T_81 on space of dimension 168. (0.04 s) Computing T_82 on space of dimension 168. Computing T_41 on space of dimension 168. (0.381 s) (0.411 s) T_83 sparse... (0.019 s). Computing T_84 on space of dimension 168. (0.029 s) Computing T_85 on space of dimension 168. (0.03 s) Computing T_86 on space of dimension 168. Computing T_43 on space of dimension 168. (0.401 s) (0.431 s) Computing T_87 on space of dimension 168. (0.03 s) Computing T_88 on space of dimension 168. (0.03 s) T_89 sparse... (0.02 s). Computing T_90 on space of dimension 168. (0.021 s) Computing T_91 on space of dimension 168. (0.039 s) Computing T_92 on space of dimension 168. (0.029 s) Computing T_93 on space of dimension 168. (0.019 s) Computing T_94 on space of dimension 168. Computing T_47 on space of dimension 168. (0.45 s) (0.47 s) Computing T_95 on space of dimension 168. (0.029 s) Computing T_96 on space of dimension 168. (0.04 s) T_97 sparse... (0.03 s). Computing T_98 on space of dimension 168. (0.02 s) Computing T_99 on space of dimension 168. (0.031 s) Computing T_100 on space of dimension 168. (0.029 s) T_101 sparse... (0.019 s). Computing T_102 on space of dimension 168. (0.019 s) T_103 sparse... (0.029 s). Computing T_104 on space of dimension 168. (0.03 s) Computing T_105 on space of dimension 168. (0.03 s) Computing T_106 on space of dimension 168. Computing T_53 on space of dimension 168. (0.49 s) (0.51 s) T_107 sparse... (0.029 s). Computing T_108 on space of dimension 168. (0.029 s) T_109 sparse... (0.029 s). Computing T_110 on space of dimension 168. (0.019 s) Computing T_111 on space of dimension 168. (0.029 s) Computing T_112 on space of dimension 168. (0.05 s) T_113 sparse... (0.03 s). Computing T_114 on space of dimension 168. (0.021 s) Computing T_115 on space of dimension 168. (0.029 s) Computing T_116 on space of dimension 168. (0.019 s) Computing T_117 on space of dimension 168. (0.039 s) Computing T_118 on space of dimension 168. Computing T_59 on space of dimension 168. (0.549 s) (0.569 s) Computing T_119 on space of dimension 168. (0.03 s) Computing T_120 on space of dimension 168. (0.041 s) Computing T_121 on space of dimension 168. (0.039 s) Computing T_122 on space of dimension 168. Computing T_61 on space of dimension 168. (0.559 s) (0.579 s) Computing T_123 on space of dimension 168. (0.03 s) Computing T_124 on space of dimension 168. (0.03 s) Computing T_125 on space of dimension 168. (0.029 s) Computing T_126 on space of dimension 168. (0.019 s) T_127 sparse... (0.029 s). Computing T_128 on space of dimension 168. (0.039 s) Computing T_129 on space of dimension 168. (0.03 s) Computing T_130 on space of dimension 168. (0.02 s) T_131 sparse... (0.03 s). Computing T_132 on space of dimension 168. (0.031 s) Computing T_133 on space of dimension 168. (0.029 s) Computing T_134 on space of dimension 168. Computing T_67 on space of dimension 168. (0.619 s) (0.649 s) Computing T_135 on space of dimension 168. (0.051 s) Computing T_136 on space of dimension 168. (0.039 s) T_137 sparse... (0.029 s). Computing T_138 on space of dimension 168. (0.029 s) T_139 sparse... (0.03 s). Computing T_140 on space of dimension 168. (0.03 s) Computing T_141 on space of dimension 168. (0.03 s) Computing T_142 on space of dimension 168. Computing T_71 on space of dimension 168. (0.651 s) (0.671 s) Computing T_143 on space of dimension 168. (0.04 s) Computing T_144 on space of dimension 168. (0.051 s) Computing T_145 on space of dimension 168. (0.029 s) Computing T_146 on space of dimension 168. Computing T_73 on space of dimension 168. (0.669 s) (0.7 s) Computing T_147 on space of dimension 168. (0.029 s) Computing T_148 on space of dimension 168. (0.029 s) T_149 sparse... (0.039 s). Computing T_150 on space of dimension 168. (0.019 s) T_151 sparse... (0.04 s). Computing T_152 on space of dimension 168. (0.03 s) Computing T_153 on space of dimension 168. (0.041 s) Computing T_154 on space of dimension 168. (0.029 s) Computing T_155 on space of dimension 168. (0.019 s) Computing T_156 on space of dimension 168. (0.029 s) T_157 sparse... (0.029 s). Computing T_158 on space of dimension 168. Computing T_79 on space of dimension 168. (0.711 s) (0.75 s) Computing T_159 on space of dimension 168. (0.03 s) Computing T_160 on space of dimension 168. (0.04 s) Computing T_161 on space of dimension 168. (0.031 s) Computing T_162 on space of dimension 168. (0.019 s) T_163 sparse... (0.039 s). Computing T_164 on space of dimension 168. (0.029 s) Computing T_165 on space of dimension 168. (0.03 s) Computing T_166 on space of dimension 168. Computing T_83 on space of dimension 168. (0.75 s) (0.78 s) T_167 sparse... (0.04 s). Computing T_168 on space of dimension 168. (0.041 s) Computing T_169 on space of dimension 168. (0.039 s) Computing T_170 on space of dimension 168. (0.019 s) Computing T_171 on space of dimension 168. (0.039 s) Computing T_172 on space of dimension 168. (0.02 s) T_173 sparse... (0.04 s). Computing T_174 on space of dimension 168. (0.031 s) Computing T_175 on space of dimension 168. (0.049 s) Computing T_176 on space of dimension 168. (0.049 s) Computing T_177 on space of dimension 168. (0.029 s) Computing T_178 on space of dimension 168. Computing T_89 on space of dimension 168. (0.8 s) (0.82 s) T_179 sparse... (0.041 s). Computing T_180 on space of dimension 168. (0.029 s) T_181 sparse... (0.039 s). Computing T_182 on space of dimension 168. (0.019 s) Computing T_183 on space of dimension 168. (0.03 s) Computing T_184 on space of dimension 168. (0.04 s) Computing T_185 on space of dimension 168. (0.031 s) Computing T_186 on space of dimension 168. (0.019 s) Computing T_187 on space of dimension 168. (0.039 s) Computing T_188 on space of dimension 168. (0.019 s) Computing T_189 on space of dimension 168. (0.049 s) Computing T_190 on space of dimension 168. (0.03 s) T_191 sparse... (0.051 s). Computing T_192 on space of dimension 168. (0.049 s) T_193 sparse... (0.049 s). Computing T_194 on space of dimension 168. Computing T_97 on space of dimension 168. (0.859 s) (0.879 s) Computing T_195 on space of dimension 168. (0.031 s) Computing T_196 on space of dimension 168. (0.029 s) T_197 sparse... (0.049 s). Computing T_198 on space of dimension 168. (0.019 s) T_199 sparse... (0.05 s). Computing T_200 on space of dimension 168. (0.04 s) Computing T_201 on space of dimension 168. (0.031 s) Computing T_202 on space of dimension 168. Computing T_101 on space of dimension 168. (0.869 s) (0.889 s) Computing T_203 on space of dimension 168. (0.03 s) Computing T_204 on space of dimension 168. (0.03 s) Computing T_205 on space of dimension 168. (0.029 s) Computing T_206 on space of dimension 168. Computing T_103 on space of dimension 168. (0.889 s) (0.909 s) Computing T_207 on space of dimension 168. (0.04 s) Computing T_208 on space of dimension 168. (0.051 s) Computing T_209 on space of dimension 168. (0.039 s) Computing T_210 on space of dimension 168. (0.019 s) T_211 sparse... (0.049 s). Computing T_212 on space of dimension 168. (0.03 s) Computing T_213 on space of dimension 168. (0.03 s) Computing T_214 on space of dimension 168. Computing T_107 on space of dimension 168. (0.939 s) (0.969 s) Computing T_215 on space of dimension 168. (0.031 s) Computing T_216 on space of dimension 168. (0.039 s) Computing T_217 on space of dimension 168. (0.029 s) Computing T_218 on space of dimension 168. Computing T_109 on space of dimension 168. (0.96 s) (0.98 s) Computing T_219 on space of dimension 168. (0.029 s) Computing T_220 on space of dimension 168. (0.02 s) Computing T_221 on space of dimension 168. (0.04 s) Computing T_222 on space of dimension 168. (0.02 s) T_223 sparse... (0.051 s). Computing T_224 on space of dimension 168. (0.049 s) Computing T_225 on space of dimension 168. (0.029 s) Computing T_226 on space of dimension 168. Computing T_113 on space of dimension 168. (0.99 s) (1.01 s) T_227 sparse... (0.05 s). Computing T_228 on space of dimension 168. (0.02 s) T_229 sparse... (0.049 s). Computing T_230 on space of dimension 168. (0.019 s) Computing T_231 on space of dimension 168. (0.029 s) Computing T_232 on space of dimension 168. (0.039 s) T_233 sparse... (0.05 s). Computing T_234 on space of dimension 168. (0.031 s) Computing T_235 on space of dimension 168. (0.019 s) Computing T_236 on space of dimension 168. (0.029 s) Computing T_237 on space of dimension 168. (0.029 s) Computing T_238 on space of dimension 168. (0.019 s) T_239 sparse... (0.05 s). Computing T_240 on space of dimension 168. (0.051 s) T_241 sparse... (0.059 s). Computing T_242 on space of dimension 168. (0.019 s) Computing T_243 on space of dimension 168. (0.039 s) Computing T_244 on space of dimension 168. (0.03 s) Computing T_245 on space of dimension 168. (0.02 s) Computing T_246 on space of dimension 168. (0.03 s) Computing T_247 on space of dimension 168. (0.041 s) Computing T_248 on space of dimension 168. (0.039 s) Computing T_249 on space of dimension 168. (0.019 s) Computing T_250 on space of dimension 168. (0.029 s) T_251 sparse... (0.06 s). Computing T_252 on space of dimension 168. (0.03 s) Computing T_253 on space of dimension 168. (0.039 s) Computing T_254 on space of dimension 168. Computing T_127 on space of dimension 168. (1.079 s) (1.099 s) Computing T_255 on space of dimension 168. (0.03 s) Computing T_256 on space of dimension 168. (0.061 s) T_257 sparse... (0.059 s). Computing T_258 on space of dimension 168. (0.029 s) Computing T_259 on space of dimension 168. (0.029 s) Computing T_260 on space of dimension 168. (0.03 s) Computing T_261 on space of dimension 168. (0.03 s) Computing T_262 on space of dimension 168. Computing T_131 on space of dimension 168. (1.091 s) (1.111 s) T_263 sparse... (0.059 s). Computing T_264 on space of dimension 168. (0.04 s) Computing T_265 on space of dimension 168. (0.03 s) Computing T_266 on space of dimension 168. (0.021 s) Computing T_267 on space of dimension 168. (0.019 s) Computing T_268 on space of dimension 168. (0.029 s) T_269 sparse... (0.059 s). Computing T_270 on space of dimension 168. (0.04 s) T_271 sparse... (0.061 s). Computing T_272 on space of dimension 168. (0.049 s) Computing T_273 on space of dimension 168. (0.019 s) Computing T_274 on space of dimension 168. Computing T_137 on space of dimension 168. (1.17 s) (1.19 s) Computing T_275 on space of dimension 168. (0.039 s) Computing T_276 on space of dimension 168. (0.029 s) T_277 sparse... (0.06 s). Computing T_278 on space of dimension 168. Computing T_139 on space of dimension 168. (1.151 s) (1.181 s) Computing T_279 on space of dimension 168. (0.03 s) Computing T_280 on space of dimension 168. (0.04 s) T_281 sparse... (0.061 s). Computing T_282 on space of dimension 168. (0.029 s) T_283 sparse... (0.069 s). Computing T_284 on space of dimension 168. (0.03 s) Computing T_285 on space of dimension 168. (0.03 s) Computing T_286 on space of dimension 168. (0.03 s) Computing T_287 on space of dimension 168. (0.029 s) Computing T_288 on space of dimension 168. (0.039 s) Computing T_289 on space of dimension 168. (0.049 s) Computing T_290 on space of dimension 168. (0.02 s) Computing T_291 on space of dimension 168. (0.03 s) Computing T_292 on space of dimension 168. (0.03 s) T_293 sparse... (0.069 s). Computing T_294 on space of dimension 168. (0.039 s) Computing T_295 on space of dimension 168. (0.029 s) Computing T_296 on space of dimension 168. (0.03 s) Computing T_297 on space of dimension 168. (0.051 s) Computing T_298 on space of dimension 168. Computing T_149 on space of dimension 168. (1.199 s) (1.219 s) Computing T_299 on space of dimension 168. (0.041 s) Computing T_300 on space of dimension 168. (0.029 s) Computing T_301 on space of dimension 168. (0.029 s) Computing T_302 on space of dimension 168. Computing T_151 on space of dimension 168. (1.23 s) (1.259 s) Computing T_303 on space of dimension 168. (0.03 s) Computing T_304 on space of dimension 168. (0.04 s) Computing T_305 on space of dimension 168. (0.031 s) Computing T_306 on space of dimension 168. (0.039 s) T_307 sparse... (0.069 s). Computing T_308 on space of dimension 168. (0.03 s) Computing T_309 on space of dimension 168. (0.03 s) Computing T_310 on space of dimension 168. (0.03 s) T_311 sparse... (0.071 s). Computing T_312 on space of dimension 168. (0.039 s) T_313 sparse... (0.069 s). Computing T_314 on space of dimension 168. Computing T_157 on space of dimension 168. (1.27 s) (1.29 s) Computing T_315 on space of dimension 168. (0.041 s) Computing T_316 on space of dimension 168. (0.029 s) T_317 sparse... (0.069 s). Computing T_318 on space of dimension 168. (0.04 s) Computing T_319 on space of dimension 168. (0.03 s) Computing T_320 on space of dimension 168. (0.051 s) Computing T_321 on space of dimension 168. (0.019 s) Computing T_322 on space of dimension 168. (0.019 s) Computing T_323 on space of dimension 168. (0.039 s) Computing T_324 on space of dimension 168. (0.03 s) Computing T_325 on space of dimension 168. (0.04 s) Computing T_326 on space of dimension 168. Computing T_163 on space of dimension 168. (1.301 s) (1.321 s) Computing T_327 on space of dimension 168. (0.029 s) Computing T_328 on space of dimension 168. (0.039 s) Computing T_329 on space of dimension 168. (0.04 s) Computing T_330 on space of dimension 168. (0.05 s) T_331 sparse... (0.081 s). Computing T_332 on space of dimension 168. (0.029 s) Computing T_333 on space of dimension 168. (0.039 s) Computing T_334 on space of dimension 168. Computing T_167 on space of dimension 168. (1.28 s) (1.31 s) Total time: 1678.789 seconds Magma V2.7-1 Mon Jan 29 2001 04:06:37 on modular [Seed = 1074697845] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2005 and weight 2.... I. Manin symbols list. (0.02 s) II. 2-term relations. (0.751 s) III. 3-term relations. Computing quotient by 804 relations. Form quot and then images (0.5 s) (total time to create space = 1.291 s) Computing cuspidal part of Full Modular symbols space of level 2005, weight 2, and dimension 202 Computing new part of Modular symbols space of level 2005, weight 2, and dimension 199. Computing 5-new part of Modular symbols space of level 2005, weight 2, and dimension 199. Computing space of modular symbols of level 401 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.11 s) III. 3-term relations. Computing quotient by 134 relations. Form quot and then images (0.04 s) (total time to create space = 0.161 s) Computing index-1 degeneracy map from level 2005 to 401. (0.139 s) Computing index-5 degeneracy map from level 2005 to 401. (0.161 s) Computing index-1 degeneracy map from level 401 to 2005. (0.589 s) Computing index-5 degeneracy map from level 401 to 2005. (0.639 s) Computing DualVectorSpace of Modular symbols space of level 2005, weight 2, and dimension 199. Computing complement of Modular symbols space of level 2005, weight 2, and dimension 199 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 202. (0.19 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 2005, weight 2, and dimension 3 Computing 401-new part of Modular symbols space of level 2005, weight 2, and dimension 199. Computing space of modular symbols of level 5 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 2005 to 5. (0.039 s) Computing index-401 degeneracy map from level 2005 to 5. (43.281 s) Computing index-1 degeneracy map from level 5 to 2005. (4.029 s) Computing index-401 degeneracy map from level 5 to 2005. (3.299 s) Finding newform decomposition of Modular symbols space of level 2005, weight 2, and dimension 199. Computing cuspidal part of Modular symbols space of level 2005, weight 2, and dimension 199 Decomposing space of level 2005 and dimension 133 using T_2. (will stop at 402) Computing T_2 on dual space of dimension 133. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^133 - 3*x^132 - 194*x^131 + 586*x^130 + 18329*x^129 - 55771*x^128 - 1123912*x^127 + 3446588*x^126 + 50293206*x^125 - 155518930*x^124 - 1750912874*x^123 + 5462635106*x^122 + 49372345330*x^121 - 155507401014*x^120 - 1159174874228*x^119 + 3688356438508*x^118 + 23118111750721*x^117 - 74364064976603*x^116 - 397612416419292*x^115 + 1293997751728436*x^114 + 5967352636688438*x^113 - 19664492236031662*x^112 - 78883287270106096*x^111 + 263457197641514212*x^110 + 925471608996089651*x^109 - 3135772582821930933*x^108 - 9696547161799726416*x^107 + 33367796092670667872*x^106 + 91197594153594434477*x^105 - 319110186086730679315*x^104 - 773259194471304076994*x^103 + 2754854109226866695954*x^102 + 5931978995426991505471*x^101 - 21548510802736535006685*x^100 - 41296067750498437248120*x^99 + 153202369999558079717256*x^98 + 261539027922364527072085*x^97 - 992669378651006608450107*x^96 - 1510004365732775805270788*x^95 + 5875155483977460694253304*x^94 + 7960890032571921898176527*x^93 - 31823062443386893001588997*x^92 - 38376301354259000516060674*x^91 + 158005280423934382718489122*x^90 + 169323999727756256389501882*x^89 - 720094935398617997645655434*x^88 - 684273481239908961774404830*x^87 + 3015593020324952235150003274*x^86 + 2533767154642437279708581536*x^85 - 11614530147765770462859605560*x^84 - 8597355586352777797212604464*x^83 + 41169023014015399706618927968*x^82 + 26724917804447034645707923012*x^81 - 134367103703108875764930409844*x^80 - 76059499707484618539219741006*x^79 + 403930724766250837224423618322*x^78 + 197979757355789614756593730722*x^77 - 1118610776326611565290461699714*x^76 - 470576245347859443880582131624*x^75 + 2853694730944228626133375534988*x^74 + 1019026975003650046386092235543*x^73 - 6705394919001690015722008252709*x^72 - 2003829735566722803250190452618*x^71 + 14507630012228473467317478937050*x^70 + 3561044454112812490261240981810*x^69 - 28888587541695594211044459380830*x^68 - 5677964909897044428907688920548*x^67 + 52911694151338467670454348486488*x^66 + 8028656345511455439133964485094*x^65 - 89072724710414345504869705024498*x^64 - 9860954299773877263871117768466*x^63 + 137692542463133629600863891951970*x^62 + 10074504886877544876489662760101*x^61 - 195246769428236454546277707137815*x^60 - 7586233817424365048312606025682*x^59 + 253645483234725819510296167334238*x^58 + 1910486576698132620264331814199*x^57 - 301456770560321718782680782243885*x^56 + 6336471012084682716127041026146*x^55 + 327250133042156804791672407849274*x^54 - 15381636224055600232060861654330*x^53 - 323895391680292967638924337145546*x^52 + 22869167576136161673194859565984*x^51 + 291686513472721744617336746748888*x^50 - 26838113067463697387442331542992*x^49 - 238465143029212437780226897093588*x^48 + 26561211682662625309167651323406*x^47 + 176531949939445391666222277071810*x^46 - 22753904430552102002751677220065*x^45 - 117997667226354775013222699915769*x^44 + 17074572554117547416424285912242*x^43 + 70988763519479441062585355088866*x^42 - 11285251871816843281582798224192*x^41 - 38301780779329299790751161866480*x^40 + 6582845870986173256498206373996*x^39 + 18459374610789903664519687090128*x^38 - 3388386814476697638619870969798*x^37 - 7910751046525643617225562218050*x^36 + 1536464211473338534949333144318*x^35 + 2999139131143033498513265801038*x^34 - 611994019440599665595235517537*x^33 - 1000054408724535503343087122993*x^32 + 213275941865031102510488915354*x^31 + 291342009487732014317264180630*x^30 - 64702395172330888234285797832*x^29 - 73585982119257557272689954056*x^28 + 16982775220050150555079066934*x^27 + 15970171750323181237337438734*x^26 - 3828109356391725129555173947*x^25 - 2946864307442598141288785923*x^24 + 734477914093752674613689588*x^23 + 456512475561793487931725396*x^22 - 118667766241202626680881047*x^21 - 58460896126803685740725227*x^20 + 15936348601364417226000876*x^19 + 6069217160918222610242212*x^18 - 1750610850075857361812326*x^17 - 497893118999044759429158*x^16 + 154181478466241570919684*x^15 + 31139587528611218838636*x^14 - 10611622615002792183614*x^13 - 1404281395029591101730*x^12 + 551766428585786070750*x^11 + 41085119885299099058*x^10 - 20690109362025539580*x^9 - 566562828020026904*x^8 + 522773823350510028*x^7 - 5101706676179664*x^6 - 7982767740504756*x^5 + 300791984854032*x^4 + 60008198977296*x^3 - 3421940825592*x^2 - 124704193383*x + 8359831557 time = 8.78 Factoring characteristic polynomial. [ , , , , , ] time = 0.51 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.001 s). Charpoly = x^2 - 2*x + 1. Decomposing space of level 2005 and dimension 2 using T_2. (will stop at 402) Computing characteristic polynomial of T_2. x^2 + 2*x + 1 time = 0.001 Factoring characteristic polynomial. [ ] time = 0.001 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Charpoly = x^2 - 6*x + 9. Decomposing space of level 2005 and dimension 2 using T_3. (will stop at 402) Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0 s). Charpoly = x^2 + 6*x + 9. Decomposing space of level 2005 and dimension 2 using T_7. (will stop at 402) Computing T_7 on dual space of dimension 2. T_7 sparse... (0 s). T_7 sparse... (0.009 s). Computing characteristic polynomial of T_7. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.001 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.001 s). Charpoly = x^2 - 2*x + 1. Decomposing space of level 2005 and dimension 2 using T_11. (will stop at 402) Computing T_11 on dual space of dimension 2. T_11 sparse... (0 s). T_11 sparse... (0.009 s). Computing characteristic polynomial of T_11. x^2 - 16 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_11), where f=x - 4. Cutting out subspace using f(T_11), where f=x + 4. Cutting out subspace using f(T_2), where f=x^3 + 3*x^2 - 3. Cutting out subspace using f(T_2), where f=x^25 + 5*x^24 - 25*x^23 - 150*x^22 + 251*x^21 + 1957*x^20 - 1241*x^19 - 14587*x^18 + 2620*x^17 + 68551*x^16 + 2150*x^15 - 211045*x^14 - 24374*x^13 + 427060*x^12 + 55015*x^11 - 552249*x^10 - 60250*x^9 + 426184*x^8 + 39117*x^7 - 171886*x^6 - 20290*x^5 + 28575*x^4 + 5729*x^3 - 936*x^2 - 259*x - 11. Cutting out subspace using f(T_2), where f=x^29 + 5*x^28 - 26*x^27 - 160*x^26 + 256*x^25 + 2235*x^24 - 935*x^23 - 17935*x^22 - 2823*x^21 + 91540*x^20 + 44746*x^19 - 310895*x^18 - 216111*x^17 + 715044*x^16 + 590210*x^15 - 1114852*x^14 - 1004451*x^13 + 1167440*x^12 + 1084091*x^11 - 808981*x^10 - 733005*x^9 + 363628*x^8 + 300934*x^7 - 102539*x^6 - 70969*x^5 + 17109*x^4 + 8582*x^3 - 1542*x^2 - 392*x + 63. Cutting out subspace using f(T_2), where f=x^37 - 11*x^36 + 2*x^35 + 398*x^34 - 1108*x^33 - 5679*x^32 + 27413*x^31 + 33805*x^30 - 336862*x^29 + 62961*x^28 + 2522330*x^27 - 2588491*x^26 - 12232569*x^25 + 21191049*x^24 + 38232747*x^23 - 99893733*x^22 - 69097784*x^21 + 310309438*x^20 + 28715603*x^19 - 659851944*x^18 + 194709056*x^17 + 963780844*x^16 - 566303318*x^15 - 946211005*x^14 + 811097812*x^13 + 587961049*x^12 - 706380307*x^11 - 192655199*x^10 + 383363223*x^9 + 1701809*x^8 - 123727562*x^7 + 22711445*x^6 + 20364125*x^5 - 7287701*x^4 - 831612*x^3 + 724676*x^2 - 109670*x + 4513. Cutting out subspace using f(T_2), where f=x^37 - 7*x^36 - 34*x^35 + 336*x^34 + 338*x^33 - 7211*x^32 + 2369*x^31 + 91305*x^30 - 96294*x^29 - 757629*x^28 + 1186170*x^27 + 4323527*x^26 - 8697717*x^25 - 17287177*x^24 + 43106935*x^23 + 48165591*x^22 - 151434960*x^21 - 89804188*x^20 + 384539897*x^19 + 97261436*x^18 - 709194538*x^17 - 17259660*x^16 + 944311478*x^15 - 122455425*x^14 - 893216626*x^13 + 204483221*x^12 + 583352933*x^11 - 165525701*x^10 - 251271583*x^9 + 75000709*x^8 + 66270538*x^7 - 18173119*x^6 - 9391349*x^5 + 2030923*x^4 + 541362*x^3 - 87822*x^2 - 8856*x + 891. Computing representation of Modular symbols space of level 2005, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on space of dimension 202. (0.07 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x p = %o, dimension = %o. 3 2 Computing T_5 on space of dimension 202. (0.099 s) Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 5 2 Computing T_7 on space of dimension 202. (0.12 s) Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x p = %o, dimension = %o. 7 2 Computing T_11 on space of dimension 202. (0.161 s) Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). %o x - 4 p = %o, dimension = %o. 11 1 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 2 Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). %o x p = %o, dimension = %o. 7 2 Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). %o x + 4 p = %o, dimension = %o. 11 1 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). %o x^3 + 3*x^2 - 3 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 25. Goal dimension = 25. Computing T_2 on dual space of dimension 25. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). %o x^25 + 5*x^24 - 25*x^23 - 150*x^22 + 251*x^21 + 1957*x^20 - 1241*x^19 - 14587*x^18 + 2620*x^17 + 68551*x^16 + 2150*x^15 - 211045*x^14 - 24374*x^13 + 427060*x^12 + 55015*x^11 - 552249*x^10 - 60250*x^9 + 426184*x^8 + 39117*x^7 - 171886*x^6 - 20290*x^5 + 28575*x^4 + 5729*x^3 - 936*x^2 - 259*x - 11 p = %o, dimension = %o. 2 25 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 29. Goal dimension = 29. Computing T_2 on dual space of dimension 29. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). %o x^29 + 5*x^28 - 26*x^27 - 160*x^26 + 256*x^25 + 2235*x^24 - 935*x^23 - 17935*x^22 - 2823*x^21 + 91540*x^20 + 44746*x^19 - 310895*x^18 - 216111*x^17 + 715044*x^16 + 590210*x^15 - 1114852*x^14 - 1004451*x^13 + 1167440*x^12 + 1084091*x^11 - 808981*x^10 - 733005*x^9 + 363628*x^8 + 300934*x^7 - 102539*x^6 - 70969*x^5 + 17109*x^4 + 8582*x^3 - 1542*x^2 - 392*x + 63 p = %o, dimension = %o. 2 29 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 37. Goal dimension = 37. Computing T_2 on dual space of dimension 37. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^37 - 11*x^36 + 2*x^35 + 398*x^34 - 1108*x^33 - 5679*x^32 + 27413*x^31 + 33805*x^30 - 336862*x^29 + 62961*x^28 + 2522330*x^27 - 2588491*x^26 - 12232569*x^25 + 21191049*x^24 + 38232747*x^23 - 99893733*x^22 - 69097784*x^21 + 310309438*x^20 + 28715603*x^19 - 659851944*x^18 + 194709056*x^17 + 963780844*x^16 - 566303318*x^15 - 946211005*x^14 + 811097812*x^13 + 587961049*x^12 - 706380307*x^11 - 192655199*x^10 + 383363223*x^9 + 1701809*x^8 - 123727562*x^7 + 22711445*x^6 + 20364125*x^5 - 7287701*x^4 - 831612*x^3 + 724676*x^2 - 109670*x + 4513 p = %o, dimension = %o. 2 37 Computing representation of Modular symbols space of level 2005, weight 2, and dimension 37. Goal dimension = 37. Computing T_2 on dual space of dimension 37. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). %o x^37 - 7*x^36 - 34*x^35 + 336*x^34 + 338*x^33 - 7211*x^32 + 2369*x^31 + 91305*x^30 - 96294*x^29 - 757629*x^28 + 1186170*x^27 + 4323527*x^26 - 8697717*x^25 - 17287177*x^24 + 43106935*x^23 + 48165591*x^22 - 151434960*x^21 - 89804188*x^20 + 384539897*x^19 + 97261436*x^18 - 709194538*x^17 - 17259660*x^16 + 944311478*x^15 - 122455425*x^14 - 893216626*x^13 + 204483221*x^12 + 583352933*x^11 - 165525701*x^10 - 251271583*x^9 + 75000709*x^8 + 66270538*x^7 - 18173119*x^6 - 9391349*x^5 + 2030923*x^4 + 541362*x^3 - 87822*x^2 - 8856*x + 891 p = %o, dimension = %o. 2 37 Computing cuspidal part of Full Modular symbols space of level 401, weight 2, and dimension 34 Computing cuspidal part of Modular symbols space of level 401, weight 2, and dimension 33 Computing new part of Modular symbols space of level 401, weight 2, and dimension 33. Computing 401-new part of Modular symbols space of level 401, weight 2, and dimension 33. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 401 and dimension 33 using T_2. (will stop at 402) Computing T_2 on dual space of dimension 33. Computing DualVectorSpace of Modular symbols space of level 401, weight 2, and dimension 33. Computing complement of Modular symbols space of level 401, weight 2, and dimension 33 Computing representation of Modular symbols space of level 401, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 34. (0.009 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 401, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^33 + 3*x^32 - 45*x^31 - 139*x^30 + 900*x^29 + 2884*x^28 - 10548*x^27 - 35418*x^26 + 80396*x^25 + 286752*x^24 - 417886*x^23 - 1613752*x^22 + 1508880*x^21 + 6487106*x^20 - 3771427*x^19 - 18852431*x^18 + 6329220*x^17 + 39643616*x^16 - 6518867*x^15 - 59770285*x^14 + 2831183*x^13 + 63307361*x^12 + 1781521*x^11 - 45478877*x^10 - 3174993*x^9 + 20925813*x^8 + 1684008*x^7 - 5616814*x^6 - 307491*x^5 + 752753*x^4 - 19364*x^3 - 39500*x^2 + 5200*x - 176 time = 0.009 Factoring characteristic polynomial. [ , ] time = 0.031 Cutting out subspace using f(T_2), where f=x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4. Cutting out subspace using f(T_2), where f=x^21 - 35*x^19 + 521*x^17 + 2*x^16 - 4305*x^15 - 51*x^14 + 21617*x^13 + 519*x^12 - 67876*x^11 - 2749*x^10 + 132085*x^9 + 8292*x^8 - 152221*x^7 - 14353*x^6 + 93934*x^5 + 12831*x^4 - 24699*x^3 - 4111*x^2 + 1058*x - 44. Computing representation of Modular symbols space of level 401, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^12 + 3*x^11 - 10*x^10 - 34*x^9 + 29*x^8 + 129*x^7 - 24*x^6 - 203*x^5 + x^4 + 130*x^3 - 5*x^2 - 22*x + 4 p = %o, dimension = %o. 2 12 Computing representation of Modular symbols space of level 401, weight 2, and dimension 21. Computing complement of Modular symbols space of level 401, weight 2, and dimension 21 Computing DualVectorSpace of Modular symbols space of level 401, weight 2, and dimension 13. Goal dimension = 13. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 13. (0.01 s) %o x^13 - 19*x^11 - 4*x^10 + 131*x^9 + 42*x^8 - 411*x^7 - 131*x^6 + 610*x^5 + 127*x^4 - 395*x^3 - 7*x^2 + 70*x - 12 p = 2, dimension = 13. Computing complement of Modular symbols space of level 401, weight 2, and dimension 13 Sorting ... 2.05 seconds. Magma: Internal error Please mail this entire run [**WITH THE FOLLOWING LINES**] to magma-bugs@maths.usyd.edu.au Version date: Tue Jul 11 14:46:05 EST 2000 Initial seed: 1074697845 Time to this point: 311.24 Segmentation fault >> -2250.out", "a"), "\n\nJ[%o] := %o ; // time = %o seconds\n\n\n", 2005, a, ^ User error: Identifier 'a' has not been declared or assigned Total time: 311.379 seconds Magma V2.7-1 Mon Jan 29 2001 04:11:49 on modular [Seed = 1141543865] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2006 and weight 2.... I. Manin symbols list. (0.05 s) II. 2-term relations. (1 s) III. 3-term relations. Computing quotient by 1080 relations. Form quot and then images (0.75 s) (total time to create space = 1.83 s) Computing cuspidal part of Full Modular symbols space of level 2006, weight 2, and dimension 274 Computing new part of Modular symbols space of level 2006, weight 2, and dimension 267. Computing 2-new part of Modular symbols space of level 2006, weight 2, and dimension 267. Computing space of modular symbols of level 1003 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.321 s) III. 3-term relations. Computing quotient by 360 relations. Form quot and then images (0.16 s) (total time to create space = 0.491 s) Computing index-1 degeneracy map from level 2006 to 1003. (0.939 s) Computing index-2 degeneracy map from level 2006 to 1003. (0.881 s) Computing index-1 degeneracy map from level 1003 to 2006. (0.75 s) Computing index-2 degeneracy map from level 1003 to 2006. (0.629 s) Computing DualVectorSpace of Modular symbols space of level 2006, weight 2, and dimension 267. Computing complement of Modular symbols space of level 2006, weight 2, and dimension 267 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 274. (0.169 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 52 Computing T_3 on space of dimension 274. (0.111 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.001 s). T_3 sparse... (0.011 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 2006, weight 2, and dimension 7 Computing 17-new part of Modular symbols space of level 2006, weight 2, and dimension 267. Computing space of modular symbols of level 118 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.051 s) III. 3-term relations. Computing quotient by 60 relations. Form quot and then images (0.009 s) (total time to create space = 0.07 s) Computing index-1 degeneracy map from level 2006 to 118. (0.08 s) Computing index-17 degeneracy map from level 2006 to 118. (0.61 s) Computing index-1 degeneracy map from level 118 to 2006. (0.929 s) Computing index-17 degeneracy map from level 118 to 2006. (1.17 s) Computing 59-new part of Modular symbols space of level 2006, weight 2, and dimension 267. Computing space of modular symbols of level 34 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.019 s) III. 3-term relations. Computing quotient by 18 relations. Form quot and then images (0 s) (total time to create space = 0.019 s) Computing index-1 degeneracy map from level 2006 to 34. (0.07 s) Computing index-59 degeneracy map from level 2006 to 34. (2.769 s) Computing index-1 degeneracy map from level 34 to 2006. (1.219 s) Computing index-59 degeneracy map from level 34 to 2006. (1.409 s) Finding newform decomposition of Modular symbols space of level 2006, weight 2, and dimension 267. Computing cuspidal part of Modular symbols space of level 2006, weight 2, and dimension 267 Decomposing space of level 2006 and dimension 79 using T_3. (will stop at 540) Computing T_3 on dual space of dimension 79. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^79 - 160*x^77 + 12230*x^75 - 594648*x^73 + 16*x^72 + 20660661*x^71 - 2280*x^70 - 546318596*x^69 + 154392*x^68 + 11433945402*x^67 - 6614184*x^66 - 194487599436*x^65 + 201355088*x^64 + 2739732828438*x^63 - 4638792112*x^62 - 32408384483300*x^61 + 84099585232*x^60 + 325278716322586*x^59 - 1231948262656*x^58 - 2792105807624528*x^57 + 14857538730928*x^56 + 20620110249450771*x^55 - 149570172557952*x^54 - 131610338685061540*x^53 + 1269931214687760*x^52 + 728381236221502722*x^51 - 9165485876594016*x^50 - 3503351950076523652*x^49 + 56563991607036256*x^48 + 14664489338046668146*x^47 - 299802658293024248*x^46 - 53452212613188788244*x^45 + 1368937204245422680*x^44 + 169636478248659475534*x^43 - 5395523891827312488*x^42 - 468342781673345980504*x^41 + 18373067667347711904*x^40 + 1123150675015101202187*x^39 - 54048994345738230760*x^38 - 2334419709637610454380*x^37 + 137207175785670526072*x^36 + 4192841559633436641070*x^35 - 299936348820899272744*x^34 - 6483467649150220643092*x^33 + 562804307511970921232*x^32 + 8591587122546627940982*x^31 - 902561559917967648608*x^30 - 9701879174208008745644*x^29 + 1230159844847842899136*x^28 + 9271578744355606523422*x^27 - 1415089540003179041424*x^26 - 7434556863137341175296*x^25 + 1362145729354201298096*x^24 + 4948553562483947048333*x^23 - 1085737228033510297200*x^22 - 2696106063273349179500*x^21 + 707398025291837084384*x^20 + 1179696102316157757590*x^19 - 370646238854854920016*x^18 - 403321278004217372444*x^17 + 152896168111454302784*x^16 + 103148724194859065953*x^15 - 48238435523957572984*x^14 - 18193914677328127548*x^13 + 11157461895648625560*x^12 + 1786637401673139892*x^11 - 1766889575684215688*x^10 + 4588640364276352*x^9 + 168068346559914480*x^8 - 22427479519293120*x^7 - 6667985341064640*x^6 + 1856047594140160*x^5 - 89387268608000*x^4 - 8746330636800*x^3 + 409723776000*x^2 time = 1.789 Factoring characteristic polynomial. [ , , , , , , , , , , , , , , , , , ] time = 0.129 Cutting out subspace using f(T_3), where f=x - 3. Cutting out subspace using f(T_3), where f=x - 2. Cutting out subspace using f(T_3), where f=x - 1. Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Charpoly = x^2 - 1. Decomposing space of level 2006 and dimension 2 using T_3. (will stop at 540) Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Charpoly = x^2 - 1. Decomposing space of level 2006 and dimension 2 using T_5. (will stop at 540) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing characteristic polynomial of T_5. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.001 s). T_5 sparse... (0.011 s). Charpoly = x^2 - 9. Decomposing space of level 2006 and dimension 2 using T_7. (will stop at 540) Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). Computing characteristic polynomial of T_7. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Charpoly = x^2 - 8*x + 7. Decomposing space of level 2006 and dimension 2 using T_11. (will stop at 540) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing characteristic polynomial of T_11. x^2 + 2*x - 24 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_11), where f=x - 4. Cutting out subspace using f(T_11), where f=x + 6. Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 5. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.001 s). T_3 sparse... (0.01 s). Charpoly = x^5 + 18*x^4 + 108*x^3 + 216*x^2. Decomposing space of level 2006 and dimension 5 using T_3. (will stop at 540) Computing characteristic polynomial of T_3. x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.001 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 5. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). Charpoly = x^5 + 8*x^4 + 16*x^3. Decomposing space of level 2006 and dimension 5 using T_5. (will stop at 540) Computing T_5 on dual space of dimension 5. T_5 sparse... (0.001 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.001 s). Computing characteristic polynomial of T_5. x^5 - 8*x^3 + 6*x^2 + 7*x - 6 time = 0 Factoring characteristic polynomial. [ , , , ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Cutting out subspace using f(T_5), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Charpoly = x^2 - 10*x + 16. Decomposing space of level 2006 and dimension 2 using T_3. (will stop at 540) Computing characteristic polynomial of T_3. x^2 + 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.001 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Charpoly = x^2 + 6*x. Decomposing space of level 2006 and dimension 2 using T_5. (will stop at 540) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.001 s). T_5 sparse... (0.011 s). Computing characteristic polynomial of T_5. x^2 - 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0.009 s). Charpoly = x^2 - 8*x + 12. Decomposing space of level 2006 and dimension 2 using T_7. (will stop at 540) Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). Computing characteristic polynomial of T_7. x^2 + 2*x + 1 time = 0.001 Factoring characteristic polynomial. [ ] time = 0.001 Cutting out subspace using f(T_7), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.001 s). T_7 sparse... (0.01 s). Charpoly = x^2 - 1. Decomposing space of level 2006 and dimension 2 using T_11. (will stop at 540) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing characteristic polynomial of T_11. x^2 + 4*x + 4 time = 0.001 Factoring characteristic polynomial. [ ] time = 0.001 Cutting out subspace using f(T_11), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.011 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Charpoly = x^2 + 24*x + 135. Decomposing space of level 2006 and dimension 2 using T_13. (will stop at 540) Computing T_13 on dual space of dimension 2. T_13 sparse... (0.009 s). T_13 sparse... (0.001 s). Computing characteristic polynomial of T_13. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_13), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Charpoly = x^2 + 22*x + 112. Decomposing space of level 2006 and dimension 2 using T_19. (will stop at 540) Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing characteristic polynomial of T_19. x^2 - 14*x + 49 time = 0.001 Factoring characteristic polynomial. [ ] time = 0.001 Cutting out subspace using f(T_19), where f=x - 7. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). Charpoly = x^2 + 36*x + 320. Decomposing space of level 2006 and dimension 2 using T_23. (will stop at 540) Computing T_23 on dual space of dimension 2. T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). Computing characteristic polynomial of T_23. x^2 - 8*x + 16 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_23), where f=x - 4. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.001 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0.011 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.009 s). T_23 sparse... (0.011 s). Charpoly = x^2 + 6*x + 8. Decomposing space of level 2006 and dimension 2 using T_29. (will stop at 540) Computing T_29 on dual space of dimension 2. T_29 sparse... (0.009 s). T_29 sparse... (0.011 s). Computing characteristic polynomial of T_29. x^2 - 6*x + 9 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_29), where f=x - 3. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.009 s). T_13 sparse... (0.001 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0 s). T_29 sparse... (0.009 s). Charpoly = x^2 - 16*x + 60. Decomposing space of level 2006 and dimension 2 using T_31. (will stop at 540) Computing T_31 on dual space of dimension 2. T_31 sparse... (0.01 s). T_31 sparse... (0.009 s). Computing characteristic polynomial of T_31. x^2 + 8*x - 20 time = 0.001 Factoring characteristic polynomial. [ , ] time = 0.001 Cutting out subspace using f(T_31), where f=x - 2. Cutting out subspace using f(T_31), where f=x + 10. Cutting out subspace using f(T_5), where f=x + 1. Cutting out subspace using f(T_5), where f=x + 3. Cutting out subspace using f(T_3), where f=x + 3. Cutting out subspace using f(T_3), where f=x^2 - x - 1. Cutting out subspace using f(T_3), where f=x^2 - 5. Cutting out subspace using f(T_3), where f=x^2 + 2*x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). Charpoly = x^4 + 24*x^3 + 180*x^2 + 432*x + 324. Decomposing space of level 2006 and dimension 4 using T_3. (will stop at 540) Computing characteristic polynomial of T_3. x^4 + 4*x^3 + 2*x^2 - 4*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x^2 + 2*x - 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Charpoly = x^4 + 12*x^3 + 50*x^2 + 84*x + 49. Decomposing space of level 2006 and dimension 4 using T_5. (will stop at 540) Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). Computing characteristic polynomial of T_5. x^4 - 4*x^3 + 8*x - 1 time = 0 Factoring characteristic polynomial. [ ] time = 0.009 Cutting out subspace using f(T_5), where f=x^4 - 4*x^3 + 8*x - 1. Cutting out subspace using f(T_3), where f=x^3 - 2*x^2 - 4*x + 7. Cutting out subspace using f(T_3), where f=x^3 + x^2 - 6*x + 2. Cutting out subspace using f(T_3), where f=x^4 - 10*x^2 + 5. Cutting out subspace using f(T_3), where f=x^4 + x^3 - 5*x^2 - 2*x + 4. Cutting out subspace using f(T_3), where f=x^4 + 3*x^3 - 4*x^2 - 9*x + 5. Cutting out subspace using f(T_3), where f=x^8 - 5*x^7 - 8*x^6 + 57*x^5 + 26*x^4 - 225*x^3 - 80*x^2 + 301*x + 149. Cutting out subspace using f(T_3), where f=x^9 + x^8 - 23*x^7 - 18*x^6 + 185*x^5 + 91*x^4 - 615*x^3 - 126*x^2 + 668*x + 44. Cutting out subspace using f(T_3), where f=x^12 + 3*x^11 - 21*x^10 - 62*x^9 + 144*x^8 + 418*x^7 - 370*x^6 - 1042*x^5 + 417*x^4 + 935*x^3 - 233*x^2 - 228*x + 62. Cutting out subspace using f(T_3), where f=x^13 - 7*x^12 - 3*x^11 + 118*x^10 - 176*x^9 - 536*x^8 + 1352*x^7 + 390*x^6 - 2933*x^5 + 1463*x^4 + 1219*x^3 - 1132*x^2 + 236*x - 8. Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on space of dimension 274. (0.149 s) Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 2 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x + 3 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^2 - x - 1 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^2 - 5 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^4 - 4*x^3 + 6*x^2 - 4*x + 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^4 + 4*x^3 + 2*x^2 - 4*x + 1 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^3 - 2*x^2 - 4*x + 7 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). %o x^3 + x^2 - 6*x + 2 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^4 - 10*x^2 + 5 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^4 + x^3 - 5*x^2 - 2*x + 4 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^4 - 4*x^3 + 6*x^2 - 4*x + 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). %o x^4 + 3*x^3 - 4*x^2 - 9*x + 5 p = %o, dimension = %o. 3 4 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^8 - 8*x^7 + 28*x^6 - 56*x^5 + 70*x^4 - 56*x^3 + 28*x^2 - 8*x + 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 8. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). %o x^8 - 5*x^7 - 8*x^6 + 57*x^5 + 26*x^4 - 225*x^3 - 80*x^2 + 301*x + 149 p = %o, dimension = %o. 3 8 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 9. Goal dimension = 9. Computing T_2 on dual space of dimension 9. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). %o x^9 + 9*x^8 + 36*x^7 + 84*x^6 + 126*x^5 + 126*x^4 + 84*x^3 + 36*x^2 + 9*x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 9. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). %o x^9 + x^8 - 23*x^7 - 18*x^6 + 185*x^5 + 91*x^4 - 615*x^3 - 126*x^2 + 668*x + 44 p = %o, dimension = %o. 3 9 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 12. Goal dimension = 12. Computing T_2 on dual space of dimension 12. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). %o x^12 + 12*x^11 + 66*x^10 + 220*x^9 + 495*x^8 + 792*x^7 + 924*x^6 + 792*x^5 + 495*x^4 + 220*x^3 + 66*x^2 + 12*x + 1 p = %o, dimension = %o. 2 40 Computing T_3 on dual space of dimension 12. T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^12 + 3*x^11 - 21*x^10 - 62*x^9 + 144*x^8 + 418*x^7 - 370*x^6 - 1042*x^5 + 417*x^4 + 935*x^3 - 233*x^2 - 228*x + 62 p = %o, dimension = %o. 3 12 Computing representation of Modular symbols space of level 2006, weight 2, and dimension 13. Goal dimension = 13. Computing T_2 on dual space of dimension 13. T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^13 - 13*x^12 + 78*x^11 - 286*x^10 + 715*x^9 - 1287*x^8 + 1716*x^7 - 1716*x^6 + 1287*x^5 - 715*x^4 + 286*x^3 - 78*x^2 + 13*x - 1 p = %o, dimension = %o. 2 39 Computing T_3 on dual space of dimension 13. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). %o x^13 - 7*x^12 - 3*x^11 + 118*x^10 - 176*x^9 - 536*x^8 + 1352*x^7 + 390*x^6 - 2933*x^5 + 1463*x^4 + 1219*x^3 - 1132*x^2 + 236*x - 8 p = %o, dimension = %o. 3 13 Computing cuspidal part of Full Modular symbols space of level 1003, weight 2, and dimension 92 Computing cuspidal part of Modular symbols space of level 1003, weight 2, and dimension 89 Computing new part of Modular symbols space of level 1003, weight 2, and dimension 89. Computing 17-new part of Modular symbols space of level 1003, weight 2, and dimension 89. Computing space of modular symbols of level 59 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.019 s) III. 3-term relations. Computing quotient by 20 relations. Form quot and then images (0 s) (total time to create space = 0.019 s) Computing index-1 degeneracy map from level 1003 to 59. (0.029 s) Computing index-17 degeneracy map from level 1003 to 59. (0.201 s) Computing index-1 degeneracy map from level 59 to 1003. (0.329 s) Computing index-17 degeneracy map from level 59 to 1003. (0.35 s) Computing DualVectorSpace of Modular symbols space of level 1003, weight 2, and dimension 89. Computing complement of Modular symbols space of level 1003, weight 2, and dimension 89 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 92. (0.019 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 1003, weight 2, and dimension 3 Computing 59-new part of Modular symbols space of level 1003, weight 2, and dimension 89. Computing space of modular symbols of level 17 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 6 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 1003 to 17. (0.019 s) Computing index-59 degeneracy map from level 1003 to 17. (1.019 s) Computing index-1 degeneracy map from level 17 to 1003. (0.37 s) Computing index-59 degeneracy map from level 17 to 1003. (0.459 s) Decomposing space of level 1003 and dimension 77 using T_2. (will stop at 540) Computing T_2 on dual space of dimension 77. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^77 + x^76 - 114*x^75 - 114*x^74 + 6215*x^73 + 6215*x^72 - 215748*x^71 - 215752*x^70 + 5357195*x^69 + 5357615*x^68 - 101336402*x^67 - 101357386*x^66 + 1518587079*x^65 + 1519251223*x^64 - 18510860890*x^63 - 18525817042*x^62 + 187007887694*x^61 + 187263058518*x^60 - 1587445327550*x^59 - 1590874627230*x^58 + 11439103009612*x^57 + 11476367260540*x^56 - 70515433067820*x^55 - 70848927395608*x^54 + 374003980995801*x^53 + 376495095688449*x^52 - 1713946399520400*x^51 - 1729631008063248*x^50 + 6806446120188500*x^49 + 6890288302671012*x^48 - 23466093247979162*x^47 - 23848583430516778*x^46 + 70295238012124632*x^45 + 71789753304394436*x^44 - 182955639957072394*x^43 - 187968210657864170*x^42 + 413319842251094422*x^41 + 427765381059019650*x^40 - 808997158450531640*x^39 - 844763148456393732*x^38 + 1368123827092227534*x^37 + 1444113697196266210*x^36 - 1991520729659692562*x^35 - 2129752665101419566*x^34 + 2483164182778598150*x^33 + 2697727227897094342*x^32 - 2635810523867232330*x^31 - 2918677112625573790*x^30 + 2363682642601295036*x^29 + 2678497759354833476*x^28 - 1773912740928126792*x^27 - 2067409815799940012*x^26 + 1101297701008711580*x^25 + 1328248791272891412*x^24 - 557604683258873472*x^23 - 701335766088736296*x^22 + 226288908586532564*x^21 + 299628717058759828*x^20 - 72095673454837696*x^19 - 101596421794390380*x^18 + 17616322015697765*x^17 + 26692769457122885*x^16 - 3230065645557866*x^15 - 5272404738335054*x^14 + 441307358677839*x^13 + 752981037560035*x^12 - 46415723441882*x^11 - 73710376511910*x^10 + 4004144325557*x^9 + 4551969054785*x^8 - 272582973312*x^7 - 151447616668*x^6 + 11235978792*x^5 + 1795165368*x^4 - 154702368*x^3 - 681264*x^2 + 54432*x time = 0.471 Factoring characteristic polynomial. [ , , , , , , , , ] time = 0.24 Cutting out subspace using f(T_2), where f=x - 2. Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Charpoly = x^4 + 12*x^3 + 54*x^2 + 108*x + 81. Decomposing space of level 1003 and dimension 4 using T_2. (will stop at 540) Computing characteristic polynomial of T_2. x^4 + 4*x^3 + 6*x^2 + 4*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Charpoly = x^4 - 4*x^3 + 6*x^2 - 4*x + 1. Decomposing space of level 1003 and dimension 4 using T_3. (will stop at 540) Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^4 - 5*x^3 + x^2 + 17*x - 6 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x - 3. Cutting out subspace using f(T_3), where f=x^3 - 2*x^2 - 5*x + 2. Cutting out subspace using f(T_2), where f=x^4 + 3*x^3 - 2*x^2 - 7*x + 1. Cutting out subspace using f(T_2), where f=x^10 + x^9 - 17*x^8 - 12*x^7 + 108*x^6 + 44*x^5 - 308*x^4 - 37*x^3 + 357*x^2 - 45*x - 81. Cutting out subspace using f(T_2), where f=x^16 + 6*x^15 - 5*x^14 - 90*x^13 - 82*x^12 + 456*x^11 + 723*x^10 - 951*x^9 - 2105*x^8 + 695*x^7 + 2641*x^6 + 151*x^5 - 1323*x^4 - 301*x^3 + 179*x^2 + 50*x - 1. Cutting out subspace using f(T_2), where f=x^18 - 5*x^17 - 16*x^16 + 112*x^15 + 52*x^14 - 984*x^13 + 431*x^12 + 4304*x^11 - 3825*x^10 - 9826*x^9 + 11533*x^8 + 11182*x^7 - 15697*x^6 - 5604*x^5 + 9201*x^4 + 1189*x^3 - 1952*x^2 - 100*x + 28. Cutting out subspace using f(T_2), where f=x^22 - 5*x^21 - 22*x^20 + 138*x^19 + 171*x^18 - 1607*x^17 - 371*x^16 + 10298*x^15 - 2353*x^14 - 39728*x^13 + 18176*x^12 + 94814*x^11 - 53292*x^10 - 138076*x^9 + 81634*x^8 + 115125*x^7 - 66881*x^6 - 46548*x^5 + 27259*x^4 + 5113*x^3 - 4430*x^2 + 540*x + 12. Computing representation of Modular symbols space of level 1003, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 4 Computing T_3 on space of dimension 92. (0.019 s) Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 3 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 4 Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^3 - 2*x^2 - 5*x + 2 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 + 3*x^3 - 2*x^2 - 7*x + 1 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 10. Goal dimension = 10. Computing T_2 on dual space of dimension 10. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^10 + x^9 - 17*x^8 - 12*x^7 + 108*x^6 + 44*x^5 - 308*x^4 - 37*x^3 + 357*x^2 - 45*x - 81 p = %o, dimension = %o. 2 10 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 16. Goal dimension = 16. Computing T_2 on dual space of dimension 16. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^16 + 6*x^15 - 5*x^14 - 90*x^13 - 82*x^12 + 456*x^11 + 723*x^10 - 951*x^9 - 2105*x^8 + 695*x^7 + 2641*x^6 + 151*x^5 - 1323*x^4 - 301*x^3 + 179*x^2 + 50*x - 1 p = %o, dimension = %o. 2 16 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 18. Goal dimension = 18. Computing T_2 on dual space of dimension 18. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^18 - 5*x^17 - 16*x^16 + 112*x^15 + 52*x^14 - 984*x^13 + 431*x^12 + 4304*x^11 - 3825*x^10 - 9826*x^9 + 11533*x^8 + 11182*x^7 - 15697*x^6 - 5604*x^5 + 9201*x^4 + 1189*x^3 - 1952*x^2 - 100*x + 28 p = %o, dimension = %o. 2 18 Computing representation of Modular symbols space of level 1003, weight 2, and dimension 22. Goal dimension = 22. Computing T_2 on dual space of dimension 22. T_2 sparse... (0 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^22 - 5*x^21 - 22*x^20 + 138*x^19 + 171*x^18 - 1607*x^17 - 371*x^16 + 10298*x^15 - 2353*x^14 - 39728*x^13 + 18176*x^12 + 94814*x^11 - 53292*x^10 - 138076*x^9 + 81634*x^8 + 115125*x^7 - 66881*x^6 - 46548*x^5 + 27259*x^4 + 5113*x^3 - 4430*x^2 + 540*x + 12 p = %o, dimension = %o. 2 22 Computing cuspidal part of Full Modular symbols space of level 118, weight 2, and dimension 17 Computing cuspidal part of Modular symbols space of level 118, weight 2, and dimension 14 Computing new part of Modular symbols space of level 118, weight 2, and dimension 14. Computing 2-new part of Modular symbols space of level 118, weight 2, and dimension 14. Computing index-1 degeneracy map from level 118 to 59. (0 s) Computing index-2 degeneracy map from level 118 to 59. (0.01 s) Computing index-1 degeneracy map from level 59 to 118. (0.051 s) Computing index-2 degeneracy map from level 59 to 118. (0.059 s) Computing DualVectorSpace of Modular symbols space of level 118, weight 2, and dimension 14. Computing complement of Modular symbols space of level 118, weight 2, and dimension 14 Computing representation of Modular symbols space of level 118, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 17. (0 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 5 Computing T_3 on space of dimension 17. (0 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 118, weight 2, and dimension 3 Computing 59-new part of Modular symbols space of level 118, weight 2, and dimension 14. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 118 to 2. (0.01 s) Computing index-59 degeneracy map from level 118 to 2. (0.291 s) Computing index-1 degeneracy map from level 2 to 118. (0.199 s) Computing index-59 degeneracy map from level 2 to 118. (0.211 s) Decomposing space of level 118 and dimension 4 using T_3. (will stop at 540) Computing T_3 on dual space of dimension 4. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^4 - 2*x^3 - 3*x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 12*x + 27. Decomposing space of level 118 and dimension 2 using T_3. (will stop at 540) Computing characteristic polynomial of T_3. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 8*x + 12. Decomposing space of level 118 and dimension 2 using T_5. (will stop at 540) Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 - 4 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Cutting out subspace using f(T_5), where f=x + 2. Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 + 6*x + 5. Decomposing space of level 118 and dimension 2 using T_3. (will stop at 540) Computing characteristic polynomial of T_3. x^2 + 2*x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 1. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 4*x - 5. Decomposing space of level 118 and dimension 2 using T_5. (will stop at 540) Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^2 + 2*x - 3 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_5), where f=x - 1. Cutting out subspace using f(T_5), where f=x + 3. Computing representation of Modular symbols space of level 118, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 118, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 118, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 118, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 2 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 1 Computing cuspidal part of Full Modular symbols space of level 59, weight 2, and dimension 6 Computing cuspidal part of Modular symbols space of level 59, weight 2, and dimension 5 Computing new part of Modular symbols space of level 59, weight 2, and dimension 5. Computing 59-new part of Modular symbols space of level 59, weight 2, and dimension 5. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 59 and dimension 5 using T_2. (will stop at 540) Computing T_2 on dual space of dimension 5. Computing DualVectorSpace of Modular symbols space of level 59, weight 2, and dimension 5. Computing complement of Modular symbols space of level 59, weight 2, and dimension 5 Computing representation of Modular symbols space of level 59, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 6. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 59, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^5 - 9*x^3 + 2*x^2 + 16*x - 8 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x^5 - 9*x^3 + 2*x^2 + 16*x - 8. Computing index-1 degeneracy map from level 59 to 2006. (1.151 s) Computing index-2 degeneracy map from level 59 to 2006. (1.089 s) Computing index-17 degeneracy map from level 59 to 2006. (1.261 s) Computing index-34 degeneracy map from level 59 to 2006. (1.299 s) Computing cuspidal part of Full Modular symbols space of level 34, weight 2, and dimension 6 Computing cuspidal part of Modular symbols space of level 34, weight 2, and dimension 3 Computing new part of Modular symbols space of level 34, weight 2, and dimension 3. Computing 2-new part of Modular symbols space of level 34, weight 2, and dimension 3. Computing index-1 degeneracy map from level 34 to 17. (0.009 s) Computing index-2 degeneracy map from level 34 to 17. (0 s) Computing index-1 degeneracy map from level 17 to 34. (0.019 s) Computing index-2 degeneracy map from level 17 to 34. (0.02 s) Computing DualVectorSpace of Modular symbols space of level 34, weight 2, and dimension 3. Goal dimension = 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 3. Computing T_2 on space of dimension 6. (0.01 s) (0.01 s) %o x^3 + x - 2 p = 2, dimension = 5. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing T_3 on space of dimension 3. Computing T_3 on space of dimension 6. (0 s) (0 s) %o x^3 + 2*x^2 p = 3, dimension = 3. Computing 17-new part of Modular symbols space of level 34, weight 2, and dimension 3. Computing index-1 degeneracy map from level 34 to 2. (0.01 s) Computing index-17 degeneracy map from level 34 to 2. (0.021 s) Computing index-1 degeneracy map from level 2 to 34. (0.049 s) Computing index-17 degeneracy map from level 2 to 34. (0.059 s) Decomposing space of level 34 and dimension 1 using T_3. (will stop at 540) Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x + 2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 2. Computing cuspidal part of Full Modular symbols space of level 17, weight 2, and dimension 2 Computing cuspidal part of Modular symbols space of level 17, weight 2, and dimension 1 Computing new part of Modular symbols space of level 17, weight 2, and dimension 1. Computing 17-new part of Modular symbols space of level 17, weight 2, and dimension 1. Decomposing space of level 17 and dimension 1 using T_2. (will stop at 540) Computing T_2 on dual space of dimension 1. Computing DualVectorSpace of Modular symbols space of level 17, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 2. (0 s) (0 s) %o x + 1 p = 2, dimension = 1. T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Computing index-1 degeneracy map from level 17 to 2006. (1.759 s) Computing index-2 degeneracy map from level 17 to 2006. (1.59 s) Computing index-59 degeneracy map from level 17 to 2006. (1.759 s) Computing index-118 degeneracy map from level 17 to 2006. (1.789 s) Sorting ... 5.53 seconds. Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.011 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.011 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.011 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.011 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 1. T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 1. T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 1. T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 1. T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 1. T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 1. T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 1. T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 1. T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.009 s). T_19 sparse... (0 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 2. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 2. T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 2. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 2. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 2. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 2. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 3. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 3. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 3. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 3. T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 3. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 3. T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 3. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). Computing T_31 on dual space of dimension 3. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 3. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 3. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 3. T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 3. T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 3. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 3. T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 3. T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 3. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 3. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 3. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 3. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). Computing T_7 on dual space of dimension 4. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 4. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 4. T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 4. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 4. T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 4. T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 4. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 4. T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 4. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 4. T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 4. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 4. T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 4. T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 4. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). Computing T_23 on dual space of dimension 4. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 4. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 4. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 4. T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 4. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 4. T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). Computing T_13 on dual space of dimension 4. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 4. T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 4. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0 s). Computing T_23 on dual space of dimension 4. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 4. T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 4. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 4. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 4. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 4. T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). Computing T_13 on dual space of dimension 4. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0 s). Computing T_17 on dual space of dimension 4. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 4. T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 4. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 4. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 4. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 4. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 8. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 8. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). Computing T_11 on dual space of dimension 8. T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 8. T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 8. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). Computing T_19 on dual space of dimension 8. T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 8. T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 8. T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 8. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 8. T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.02 s). Computing T_5 on dual space of dimension 9. T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 9. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 9. T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 9. T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 9. T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 9. T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 9. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). Computing T_29 on dual space of dimension 9. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). Computing T_31 on dual space of dimension 9. T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). Computing T_37 on dual space of dimension 9. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). Computing T_5 on dual space of dimension 12. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 12. T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing T_11 on dual space of dimension 12. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 12. T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). Computing T_17 on dual space of dimension 12. T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). Computing T_19 on dual space of dimension 12. T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.011 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). Computing T_23 on dual space of dimension 12. T_23 sparse... (0 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). Computing T_29 on dual space of dimension 12. T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 12. T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 12. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). Computing T_5 on dual space of dimension 13. T_5 sparse... (0.011 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 13. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0 s). T_7 sparse... (0 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Computing T_11 on dual space of dimension 13. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). T_11 sparse... (0.011 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0.009 s). T_11 sparse... (0 s). T_11 sparse... (0 s). T_11 sparse... (0.01 s). Computing T_13 on dual space of dimension 13. T_13 sparse... (0 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). T_13 sparse... (0.011 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.009 s). T_13 sparse... (0.01 s). T_13 sparse... (0.01 s). Computing T_17 on dual space of dimension 13. T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.011 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.009 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). T_17 sparse... (0.01 s). Computing T_19 on dual space of dimension 13. T_19 sparse... (0 s). T_19 sparse... (0 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.009 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). T_19 sparse... (0.01 s). Computing T_23 on dual space of dimension 13. T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.009 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.01 s). T_23 sparse... (0.011 s). Computing T_29 on dual space of dimension 13. T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.01 s). T_29 sparse... (0.011 s). T_29 sparse... (0.009 s). T_29 sparse... (0.009 s). Computing T_31 on dual space of dimension 13. T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.01 s). T_31 sparse... (0.011 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). T_31 sparse... (0.009 s). Computing T_37 on dual space of dimension 13. T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.01 s). T_37 sparse... (0.011 s). T_37 sparse... (0.019 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.009 s). T_37 sparse... (0.01 s). Computing q-expansion. T_2 sparse... (0.009 s). T_3 sparse... (0 s). T_5 sparse... (0.009 s). T_7 sparse... (0.009 s). T_11 sparse... (0.009 s). T_13 sparse... (0 s). T_17 sparse... (0 s). T_19 sparse... (0 s). T_23 sparse... (0.01 s). T_29 sparse... (0.01 s). T_31 sparse... (0.01 s). T_37 sparse... (0.01 s). (0.129 s) Computing q-expansion. (0.019 s) Computing q-expansion. T_2 sparse... (0.009 s). T_3 sparse... (0 s). T_5 sparse... (0.009 s). T_7 sparse... (0.009 s). T_11 sparse... (0.009 s). T_13 sparse... (0.01 s). T_17 sparse... (0 s). T_19 sparse... (0 s). T_23 sparse... (0.01 s). T_29 sparse... (0.01 s). T_31 sparse... (0.01 s). T_37 sparse... (0.011 s). (0.11 s) Computing q-expansion. (0.009 s) Computing q-expansion. (0.019 s) Computing q-expansion. (0.009 s) Computing q-expansion. (0.01 s) Computing q-expansion. (0.02 s) Computing q-expansion. (0.01 s) Computing q-expansion. (0.021 s) Computing q-expansion. (0.009 s) Computing q-expansion. (0.029 s) Computing q-expansion. (0.03 s) Computing q-expansion. (0.031 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.041 s) Computing q-expansion. (0.029 s) Computing q-expansion. (0.03 s) Computing q-expansion. (0.029 s) Computing q-expansion. (0.089 s) Computing q-expansion. (0.039 s) Computing q-expansion. (0.059 s) Computing q-expansion. (0.049 s) Computing character group of torus of J_0(2*1003)/F_2. 92.9 seconds. Computing T_2 on space of dimension 1. (0.009 s) Computing T_3 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing character group of torus of J_0(17*118)/F_17. 541.551 seconds. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing character group of torus of J_0(59*34)/F_59. 642.08 seconds. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.01 s) Computing T_3 on space of dimension 1. (0.01 s) Computing T_5 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.009 s) Computing T_3 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_5 on space of dimension 1. (0.01 s) WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0 s) Computing T_3 on space of dimension 1. (0.021 s) Computing T_5 on space of dimension 1. (0.02 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.009 s) Computing T_3 on space of dimension 1. (0.009 s) Computing T_5 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.009 s) Computing T_3 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.01 s) Computing T_3 on space of dimension 1. (0.009 s) Computing T_5 on space of dimension 1. (0.01 s) Computing T_7 on space of dimension 1. Computing T_7 on space of dimension 274. (0.19 s) (0.201 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.009 s) Computing T_3 on space of dimension 1. (0.009 s) Computing T_5 on space of dimension 1. (0.009 s) Computing T_7 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.01 s) Computing T_3 on space of dimension 1. (0.009 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_5 on space of dimension 1. (0.01 s) WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.01 s) Computing T_3 on space of dimension 1. (0.009 s) Computing T_5 on space of dimension 1. (0.02 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 1. (0.009 s) Computing T_3 on space of dimension 1. (0.01 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 2. (0.01 s) Computing T_3 on space of dimension 2. (0.021 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 2. (0.019 s) Computing T_3 on space of dimension 2. (0.03 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 3. (0.02 s) Computing T_3 on space of dimension 3. (0.03 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 3. (0.029 s) Computing T_3 on space of dimension 3. (0.03 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 4. (0.041 s) Computing T_3 on space of dimension 4. (0.04 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 4. (0.03 s) Computing T_3 on space of dimension 4. (0.039 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 4. (0.03 s) Computing T_3 on space of dimension 4. (0.039 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 4. (0.039 s) Computing T_3 on space of dimension 4. (0.049 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 8. (0.069 s) Computing T_3 on space of dimension 8. (0.08 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 9. (0.07 s) Computing T_3 on space of dimension 9. (0.079 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 12. (0.09 s) Computing T_3 on space of dimension 12. (0.11 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_2 on space of dimension 13. (0.099 s) Computing T_3 on space of dimension 13. (0.11 s) WARNING: Because working in +1 or -1 quotient, the modular degree is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. WARNING: Because working in +1 or -1 quotient, the component group order is only correct up to a power of 2. Computing T_5 on space of dimension 1. (0.009 s) Computing T_7 on space of dimension 1. (0.01 s) Computing T_11 on space of dimension 1. Computing T_11 on space of dimension 274. (0.269 s) (0.289 s) Computing T_13 on space of dimension 1. Computing T_13 on space of dimension 274. (0.321 s) (0.331 s) Computing T_19 on space of dimension 1. Computing T_19 on space of dimension 274. (0.46 s) (0.48 s) Computing T_23 on space of dimension 1. Computing T_23 on space of dimension 274. (0.56 s) (0.57 s) Computing T_29 on space of dimension 1. Computing T_29 on space of dimension 274. (0.69 s) (0.71 s) Computing T_31 on space of dimension 1. Computing T_31 on space of dimension 274. (0.759 s) (0.779 s) Computing T_37 on space of dimension 1. Computing T_37 on space of dimension 274. (0.911 s) (0.931 s) Computing T_7 on space of dimension 1. (0.009 s) Computing T_11 on space of dimension 1. (0.02 s) Computing T_13 on space of dimension 1. (0.01 s) Computing T_19 on space of dimension 1. (0.019 s) Computing T_23 on space of dimension 1. (0.009 s) Computing T_29 on space of dimension 1. (0.02 s) Computing T_31 on space of dimension 1. (0.02 s) Computing T_37 on space of dimension 1. (0.02 s) Computing T_7 on space of dimension 1. (0.01 s) Computing T_11 on space of dimension 1. (0.009 s) Computing T_13 on space of dimension 1. (0.02 s) Computing T_19 on space of dimension 1. (0.021 s) Computing T_23 on space of dimension 1. (0.009 s) Computing T_29 on space of dimension 1. (0.021 s) Computing T_31 on space of dimension 1. (0.02 s) Computing T_37 on space of dimension 1. (0.01 s) Computing T_7 on space of dimension 1. (0.01 s) Computing T_11 on space of dimension 1. (0.009 s) Computing T_13 on space of dimension 1. (0.02 s) Computing T_19 on space of dimension 1. (0.02 s) Computing T_23 on space of dimension 1. (0.01 s) Computing T_29 on space of dimension 1. (0.019 s) Computing T_31 on space of dimension 1. (0.019 s) Computing T_37 on space of dimension 1. (0.019 s) Computing T_7 on space of dimension 1. (0.009 s) Computing T_11 on space of dimension 1. (0.02 s) Computing T_13 on space of dimension 1. (0.01 s) Computing T_19 on space of dimension 1. (0.019 s) Computing T_23 on space of dimension 1. (0.021 s) Computing T_29 on space of dimension 1. (0.01 s) Computing T_31 on space of dimension 1. (0.019 s) Computing T_37 on space of dimension 1. (0.019 s) Computing T_5 on space of dimension 1. (0.009 s) Computing T_7 on space of dimension 1. (0.01 s) Computing T_11 on space of dimension 1. (0.019 s) Computing T_13 on space of dimension 1. (0.009 s) Computing T_19 on space of dimension 1. (0.02 s) Computing T_23 on space of dimension 1. (0.02 s) Computing T_29 on space of dimension 1. (0.01 s) Computing T_31 on space of dimension 1. (0.019 s) Computing T_37 on space of dimension 1. (0.019 s) Computing T_11 on space of dimension 1. (0.019 s) Computing T_13 on space of dimension 1. (0.01 s) Computing T_19 on space of dimension 1. (0.019 s) Computing T_23 on space of dimension 1. (0.019 s) Computing T_29 on space of dimension 1. (0.009 s) Computing T_31 on space of dimension 1. (0.02 s) Computing T_37 on space of dimension 1. (0.02 s) Computing T_11 on space of dimension 1. (0.02 s) Computing T_13 on space of dimension 1. (0.01 s) Computing T_19 on space of dimension 1. (0.019 s) Computing T_23 on space of dimension 1. (0.019 s) Computing T_29 on space of dimension 1. (0.009 s) Computing T_31 on space of dimension 1. (0.02 s) Computing T_37 on space of dimension 1. (0.02 s) Computing T_7 on space of dimension 1. (0.01 s) Computing T_11 on space of dimension 1. (0.019 s) Computing T_13 on space of dimension 1. (0.01 s) Computing T_19 on space of dimension 1. (0.019 s) Computing T_23 on space of dimension 1. (0.019 s) Computing T_29 on space of dimension 1. (0.009 s) Computing T_31 on space of dimension 1. (0.02 s) Computing T_37 on space of dimension 1. (0.02 s) Computing T_7 on space of dimension 1. (0.01 s) Computing T_11 on space of dimension 1. (0.019 s) Computing T_13 on space of dimension 1. (0.009 s) Computing T_19 on space of dimension 1. (0.02 s) Computing T_23 on space of dimension 1. (0.01 s) Computing T_29 on space of dimension 1. (0.019 s) Computing T_31 on space of dimension 1. (0.019 s) Computing T_37 on space of dimension 1. (0.009 s) Computing T_5 on space of dimension 1. (0.01 s) Computing T_7 on space of dimension 1. (0.019 s) Computing T_11 on space of dimension 1. (0.01 s) Computing T_13 on space of dimension 1. (0.019 s) Computing T_19 on space of dimension 1. (0.019 s) Computing T_23 on space of dimension 1. (0.009 s) Computing T_29 on space of dimension 1. (0.02 s) Computing T_31 on space of dimension 1. (0.02 s) Computing T_37 on space of dimension 1. (0.01 s) Computing T_5 on space of dimension 2. (0.02 s) Computing T_7 on space of dimension 2. (0.02 s) Computing T_11 on space of dimension 2. (0.03 s) Computing T_13 on space of dimension 2. (0.029 s) Computing T_19 on space of dimension 2. (0.03 s) Computing T_23 on space of dimension 2. (0.039 s) Computing T_29 on space of dimension 2. (0.03 s) Computing T_31 on space of dimension 2. (0.029 s) Computing T_37 on space of dimension 2. (0.029 s) Computing T_5 on space of dimension 2. (0.03 s) Computing T_7 on space of dimension 2. (0.029 s) Computing T_11 on space of dimension 2. (0.03 s) Computing T_13 on space of dimension 2. (0.039 s) Computing T_19 on space of dimension 2. (0.041 s) Computing T_23 on space of dimension 2. (0.039 s) Computing T_29 on space of dimension 2. (0.039 s) Computing T_31 on space of dimension 2. (0.039 s) Computing T_37 on space of dimension 2. (0.049 s) Computing T_5 on space of dimension 3. (0.03 s) Computing T_7 on space of dimension 3. (0.041 s) Computing T_11 on space of dimension 3. (0.04 s) Computing T_13 on space of dimension 3. (0.05 s) Computing T_19 on space of dimension 3. (0.049 s) Computing T_23 on space of dimension 3. (0.05 s) Computing T_29 on space of dimension 3. (0.05 s) Computing T_31 on space of dimension 3. (0.049 s) Computing T_37 on space of dimension 3. (0.05 s) Computing T_5 on space of dimension 3. (0.039 s) Computing T_7 on space of dimension 3. (0.039 s) Computing T_11 on space of dimension 3. (0.059 s) Computing T_13 on space of dimension 3. (0.05 s) Computing T_19 on space of dimension 3. (0.059 s) Computing T_23 on space of dimension 3. (0.059 s) Computing T_29 on space of dimension 3. (0.059 s) Computing T_31 on space of dimension 3. (0.061 s) Computing T_37 on space of dimension 3. (0.06 s) Computing T_5 on space of dimension 4. (0.05 s) Computing T_7 on space of dimension 4. (0.059 s) Computing T_11 on space of dimension 4. (0.059 s) Computing T_13 on space of dimension 4. (0.06 s) Computing T_19 on space of dimension 4. (0.07 s) Computing T_23 on space of dimension 4. (0.07 s) Computing T_29 on space of dimension 4. (0.079 s) Computing T_31 on space of dimension 4. (0.069 s) Computing T_37 on space of dimension 4. (0.07 s) Computing T_5 on space of dimension 4. (0.05 s) Computing T_7 on space of dimension 4. (0.039 s) Computing T_11 on space of dimension 4. (0.05 s) Computing T_13 on space of dimension 4. (0.059 s) Computing T_19 on space of dimension 4. (0.059 s) Computing T_23 on space of dimension 4. (0.07 s) Computing T_29 on space of dimension 4. (0.059 s) Computing T_31 on space of dimension 4. (0.069 s) Computing T_37 on space of dimension 4. (0.061 s) Computing T_5 on space of dimension 4. (0.041 s) Computing T_7 on space of dimension 4. (0.05 s) Computing T_11 on space of dimension 4. (0.059 s) Computing T_13 on space of dimension 4. (0.059 s) Computing T_19 on space of dimension 4. (0.07 s) Computing T_23 on space of dimension 4. (0.069 s) Computing T_29 on space of dimension 4. (0.06 s) Computing T_31 on space of dimension 4. (0.07 s) Computing T_37 on space of dimension 4. (0.07 s) Computing T_5 on space of dimension 4. (0.049 s) Computing T_7 on space of dimension 4. (0.049 s) Computing T_11 on space of dimension 4. (0.07 s) Computing T_13 on space of dimension 4. (0.079 s) Computing T_19 on space of dimension 4. (0.089 s) Computing T_23 on space of dimension 4. (0.09 s) Computing T_29 on space of dimension 4. (0.091 s) Computing T_31 on space of dimension 4. (0.089 s) Computing T_37 on space of dimension 4. (0.09 s) Computing T_5 on space of dimension 8. (0.1 s) Computing T_7 on space of dimension 8. (0.11 s) Computing T_11 on space of dimension 8. (0.119 s) Computing T_13 on space of dimension 8. (0.13 s) Computing T_19 on space of dimension 8. (0.13 s) Computing T_23 on space of dimension 8. (0.13 s) Computing T_29 on space of dimension 8. (0.139 s) Computing T_31 on space of dimension 8. (0.139 s) Computing T_37 on space of dimension 8. (0.14 s) Computing T_5 on space of dimension 9. (0.099 s) Computing T_7 on space of dimension 9. (0.11 s) Computing T_11 on space of dimension 9. (0.13 s) Computing T_13 on space of dimension 9. (0.12 s) Computing T_19 on space of dimension 9. (0.15 s) Computing T_23 on space of dimension 9. (0.15 s) Computing T_29 on space of dimension 9. (0.139 s) Computing T_31 on space of dimension 9. (0.15 s) Computing T_37 on space of dimension 9. (0.151 s) Computing T_5 on space of dimension 12. (0.13 s) Computing T_7 on space of dimension 12. (0.139 s) Computing T_11 on space of dimension 12. (0.17 s) Computing T_13 on space of dimension 12. (0.181 s) Computing T_19 on space of dimension 12. (0.179 s) Computing T_23 on space of dimension 12. (0.199 s) Computing T_29 on space of dimension 12. (0.199 s) Computing T_31 on space of dimension 12. (0.19 s) Computing T_37 on space of dimension 12. (0.201 s) Computing T_5 on space of dimension 13. (0.14 s) Computing T_7 on space of dimension 13. (0.15 s) Computing T_11 on space of dimension 13. (0.179 s) Computing T_13 on space of dimension 13. (0.19 s) Computing T_19 on space of dimension 13. (0.199 s) Computing T_23 on space of dimension 13. (0.21 s) Computing T_29 on space of dimension 13. (0.201 s) Computing T_31 on space of dimension 13. (0.21 s) Computing T_37 on space of dimension 13. (0.21 s) Computing T_1 on space of dimension 274. (0 s) T_2 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_4 on space of dimension 274. (0.06 s) T_5 sparse... (0 s). Computing T_6 on space of dimension 274. (0.039 s) T_7 sparse... (0.01 s). Computing T_8 on space of dimension 274. (0.069 s) Computing T_9 on space of dimension 274. (0.079 s) Computing T_10 on space of dimension 274. (0.05 s) T_11 sparse... (0 s). Computing T_12 on space of dimension 274. (0.06 s) T_13 sparse... (0.009 s). Computing T_14 on space of dimension 274. (0.05 s) Computing T_15 on space of dimension 274. (0.059 s) Computing T_16 on space of dimension 274. (0.079 s) T_17 sparse... (0.01 s). Computing T_18 on space of dimension 274. (0.059 s) T_19 sparse... (0.01 s). Computing T_20 on space of dimension 274. (0.059 s) Computing T_21 on space of dimension 274. (0.06 s) Computing T_22 on space of dimension 274. (0.05 s) T_23 sparse... (0.009 s). Computing T_24 on space of dimension 274. (0.07 s) Computing T_25 on space of dimension 274. (0.099 s) Computing T_26 on space of dimension 274. (0.059 s) Computing T_27 on space of dimension 274. (0.101 s) Computing T_28 on space of dimension 274. (0.07 s) T_29 sparse... (0.01 s). Computing T_30 on space of dimension 274. (0.059 s) T_31 sparse... (0.01 s). Computing T_32 on space of dimension 274. (0.069 s) Computing T_33 on space of dimension 274. (0.07 s) Computing T_34 on space of dimension 274. Computing T_17 on space of dimension 274. (0.679 s) (0.739 s) Computing T_35 on space of dimension 274. (0.079 s) Computing T_36 on space of dimension 274. (0.07 s) T_37 sparse... (0.01 s). Computing T_38 on space of dimension 274. (0.059 s) Computing T_39 on space of dimension 274. (0.07 s) Computing T_40 on space of dimension 274. (0.069 s) T_41 sparse... (0.01 s). Computing T_42 on space of dimension 274. (0.05 s) T_43 sparse... (0.009 s). Computing T_44 on space of dimension 274. (0.059 s) Computing T_45 on space of dimension 274. (0.12 s) Computing T_46 on space of dimension 274. (0.059 s) T_47 sparse... (0.02 s). Computing T_48 on space of dimension 274. (0.09 s) Computing T_49 on space of dimension 274. (0.119 s) Computing T_50 on space of dimension 274. (0.06 s) Computing T_51 on space of dimension 274. (0.069 s) Computing T_52 on space of dimension 274. (0.061 s) T_53 sparse... (0.019 s). Computing T_54 on space of dimension 274. (0.059 s) Computing T_55 on space of dimension 274. (0.09 s) Computing T_56 on space of dimension 274. (0.079 s) Computing T_57 on space of dimension 274. (0.069 s) Computing T_58 on space of dimension 274. (0.06 s) T_59 sparse... (0.009 s). Computing T_60 on space of dimension 274. (0.059 s) T_61 sparse... (0.019 s). Computing T_62 on space of dimension 274. (0.059 s) Computing T_63 on space of dimension 274. (0.13 s) Computing T_64 on space of dimension 274. (0.08 s) Computing T_65 on space of dimension 274. (0.09 s) Computing T_66 on space of dimension 274. (0.059 s) T_67 sparse... (0.02 s). Computing T_68 on space of dimension 274. (0.07 s) Computing T_69 on space of dimension 274. (0.07 s) Computing T_70 on space of dimension 274. (0.06 s) T_71 sparse... (0.019 s). Computing T_72 on space of dimension 274. (0.089 s) T_73 sparse... (0.019 s). Computing T_74 on space of dimension 274. (0.059 s) Computing T_75 on space of dimension 274. (0.07 s) Computing T_76 on space of dimension 274. (0.07 s) Computing T_77 on space of dimension 274. (0.111 s) Computing T_78 on space of dimension 274. (0.06 s) T_79 sparse... (0.02 s). Computing T_80 on space of dimension 274. (0.11 s) Computing T_81 on space of dimension 274. (0.109 s) Computing T_82 on space of dimension 274. Computing T_41 on space of dimension 274. (1.019 s) (1.079 s) T_83 sparse... (0.02 s). Computing T_84 on space of dimension 274. (0.07 s) Computing T_85 on space of dimension 274. (0.079 s) Computing T_86 on space of dimension 274. Computing T_43 on space of dimension 274. (1.06 s) (1.13 s) Computing T_87 on space of dimension 274. (0.07 s) Computing T_88 on space of dimension 274. (0.091 s) T_89 sparse... (0.03 s). Computing T_90 on space of dimension 274. (0.11 s) Computing T_91 on space of dimension 274. (0.111 s) Computing T_92 on space of dimension 274. (0.059 s) Computing T_93 on space of dimension 274. (0.07 s) Computing T_94 on space of dimension 274. Computing T_47 on space of dimension 274. (1.159 s) (1.219 s) Computing T_95 on space of dimension 274. (0.09 s) Computing T_96 on space of dimension 274. (0.119 s) T_97 sparse... (0.029 s). Computing T_98 on space of dimension 274. (0.06 s) Computing T_99 on space of dimension 274. (0.13 s) Computing T_100 on space of dimension 274. (0.06 s) T_101 sparse... (0.03 s). Computing T_102 on space of dimension 274. (0.11 s) T_103 sparse... (0.03 s). Computing T_104 on space of dimension 274. (0.079 s) Computing T_105 on space of dimension 274. (0.069 s) Computing T_106 on space of dimension 274. Computing T_53 on space of dimension 274. (1.34 s) (1.4 s) T_107 sparse... (0.03 s). Computing T_108 on space of dimension 274. (0.07 s) T_109 sparse... (0.019 s). Computing T_110 on space of dimension 274. (0.1 s) Computing T_111 on space of dimension 274. (0.07 s) Computing T_112 on space of dimension 274. (0.111 s) T_113 sparse... (0.03 s). Computing T_114 on space of dimension 274. (0.099 s) Computing T_115 on space of dimension 274. (0.1 s) Computing T_116 on space of dimension 274. (0.069 s) Computing T_117 on space of dimension 274. (0.141 s) Computing T_118 on space of dimension 274. Computing T_59 on space of dimension 274. (3.159 s) (3.259 s) Computing T_119 on space of dimension 274. (0.101 s) Computing T_120 on space of dimension 274. (0.079 s) Computing T_121 on space of dimension 274. (0.17 s) Computing T_122 on space of dimension 274. Computing T_61 on space of dimension 274. (1.54 s) (1.61 s) Computing T_123 on space of dimension 274. (0.081 s) Computing T_124 on space of dimension 274. (0.069 s) Computing T_125 on space of dimension 274. (0.119 s) Computing T_126 on space of dimension 274. (0.101 s) T_127 sparse... (0.03 s). Computing T_128 on space of dimension 274. (0.13 s) Computing T_129 on space of dimension 274. (0.069 s) Computing T_130 on space of dimension 274. (0.11 s) T_131 sparse... (0.03 s). Computing T_132 on space of dimension 274. (0.069 s) Computing T_133 on space of dimension 274. (0.139 s) Computing T_134 on space of dimension 274. Computing T_67 on space of dimension 274. (1.69 s) (1.8 s) Computing T_135 on space of dimension 274. (0.23 s) Computing T_136 on space of dimension 274. (0.079 s) T_137 sparse... (0.03 s). Computing T_138 on space of dimension 274. (0.109 s) T_139 sparse... (0.03 s). Computing T_140 on space of dimension 274. (0.07 s) Computing T_141 on space of dimension 274. (0.079 s) Computing T_142 on space of dimension 274. Computing T_71 on space of dimension 274. (1.779 s) (1.889 s) Computing T_143 on space of dimension 274. (0.159 s) Computing T_144 on space of dimension 274. (0.121 s) Computing T_145 on space of dimension 274. (0.12 s) Computing T_146 on space of dimension 274. Computing T_73 on space of dimension 274. (1.829 s) (1.94 s) Computing T_147 on space of dimension 274. (0.079 s) Computing T_148 on space of dimension 274. (0.081 s) T_149 sparse... (0.04 s). Computing T_150 on space of dimension 274. (0.11 s) T_151 sparse... (0.03 s). Computing T_152 on space of dimension 274. (0.1 s) Computing T_153 on space of dimension 274. (0.21 s) Computing T_154 on space of dimension 274. (0.109 s) Computing T_155 on space of dimension 274. (0.09 s) Computing T_156 on space of dimension 274. (0.069 s) T_157 sparse... (0.04 s). Computing T_158 on space of dimension 274. Computing T_79 on space of dimension 274. (2.01 s) (2.11 s) Computing T_159 on space of dimension 274. (0.07 s) Computing T_160 on space of dimension 274. (0.15 s) Computing T_161 on space of dimension 274. (0.109 s) Computing T_162 on space of dimension 274. (0.099 s) T_163 sparse... (0.039 s). Computing T_164 on space of dimension 274. (0.069 s) Computing T_165 on space of dimension 274. (0.169 s) Computing T_166 on space of dimension 274. Computing T_83 on space of dimension 274. (2.07 s) (2.181 s) T_167 sparse... (0.04 s). Computing T_168 on space of dimension 274. (0.079 s) Computing T_169 on space of dimension 274. (0.18 s) Computing T_170 on space of dimension 274. (0.11 s) Computing T_171 on space of dimension 274. (0.21 s) Computing T_172 on space of dimension 274. (0.07 s) T_173 sparse... (0.039 s). Computing T_174 on space of dimension 274. (0.11 s) Computing T_175 on space of dimension 274. (0.219 s) Computing T_176 on space of dimension 274. (0.11 s) Computing T_177 on space of dimension 274. (0.159 s) Computing T_178 on space of dimension 274. Computing T_89 on space of dimension 274. (2.26 s) (2.38 s) T_179 sparse... (0.049 s). Computing T_180 on space of dimension 274. (0.17 s) T_181 sparse... (0.049 s). Computing T_182 on space of dimension 274. (0.11 s) Computing T_183 on space of dimension 274. (0.07 s) Computing T_184 on space of dimension 274. (0.079 s) Computing T_185 on space of dimension 274. (0.089 s) Computing T_186 on space of dimension 274. (0.11 s) Computing T_187 on space of dimension 274. (0.139 s) Computing T_188 on space of dimension 274. (0.071 s) Computing T_189 on space of dimension 274. (0.239 s) Computing T_190 on space of dimension 274. (0.11 s) T_191 sparse... (0.05 s). Computing T_192 on space of dimension 274. (0.61 s) T_193 sparse... (0.05 s). Computing T_194 on space of dimension 274. Computing T_97 on space of dimension 274. (2.42 s) (2.529 s) Computing T_195 on space of dimension 274. (0.159 s) Computing T_196 on space of dimension 274. (0.07 s) T_197 sparse... (0.051 s). Computing T_198 on space of dimension 274. (0.119 s) T_199 sparse... (0.05 s). Computing T_200 on space of dimension 274. (0.09 s) Computing T_201 on space of dimension 274. (0.17 s) Computing T_202 on space of dimension 274. Computing T_101 on space of dimension 274. (2.48 s) (2.6 s) Computing T_203 on space of dimension 274. (0.11 s) Computing T_204 on space of dimension 274. (0.149 s) Computing T_205 on space of dimension 274. (0.101 s) Computing T_206 on space of dimension 274. Computing T_103 on space of dimension 274. (2.509 s) (2.63 s) Computing T_207 on space of dimension 274. (0.13 s) Computing T_208 on space of dimension 274. (0.119 s) Computing T_209 on space of dimension 274. (0.15 s) Computing T_210 on space of dimension 274. (0.11 s) T_211 sparse... (0.049 s). Computing T_212 on space of dimension 274. (0.07 s) Computing T_213 on space of dimension 274. (0.17 s) Computing T_214 on space of dimension 274. Computing T_107 on space of dimension 274. (2.63 s) (2.73 s) Computing T_215 on space of dimension 274. (0.1 s) Computing T_216 on space of dimension 274. (0.09 s) Computing T_217 on space of dimension 274. (0.109 s) Computing T_218 on space of dimension 274. Computing T_109 on space of dimension 274. (2.61 s) (2.721 s) Computing T_219 on space of dimension 274. (0.17 s) Computing T_220 on space of dimension 274. (0.159 s) Computing T_221 on space of dimension 274. (0.15 s) Computing T_222 on space of dimension 274. (0.099 s) T_223 sparse... (0.06 s). Computing T_224 on space of dimension 274. (0.181 s) Computing T_225 on space of dimension 274. (0.17 s) Computing T_226 on space of dimension 274. Computing T_113 on space of dimension 274. (2.759 s) (2.879 s) T_227 sparse... (0.059 s). Computing T_228 on space of dimension 274. (0.159 s) T_229 sparse... (0.059 s). Computing T_230 on space of dimension 274. (0.11 s) Computing T_231 on space of dimension 274. (0.181 s) Computing T_232 on space of dimension 274. (0.091 s) T_233 sparse... (0.059 s). Computing T_234 on space of dimension 274. (0.11 s) Computing T_235 on space of dimension 274. (0.099 s) Computing T_236 on space of dimension 274. (0.15 s) Computing T_237 on space of dimension 274. (0.17 s) Computing T_238 on space of dimension 274. (0.12 s) T_239 sparse... (0.059 s). Computing T_240 on space of dimension 274. (0.13 s) T_241 sparse... (0.07 s). Computing T_242 on space of dimension 274. (0.11 s) Computing T_243 on space of dimension 274. (0.199 s) Computing T_244 on space of dimension 274. (0.07 s) Computing T_245 on space of dimension 274. (0.09 s) Computing T_246 on space of dimension 274. (0.099 s) Computing T_247 on space of dimension 274. (0.21 s) Computing T_248 on space of dimension 274. (0.08 s) Computing T_249 on space of dimension 274. (0.17 s) Computing T_250 on space of dimension 274. (0.109 s) T_251 sparse... (0.061 s). Computing T_252 on space of dimension 274. (0.15 s) Computing T_253 on space of dimension 274. (0.15 s) Computing T_254 on space of dimension 274. Computing T_127 on space of dimension 274. (3 s) (3.121 s) Computing T_255 on space of dimension 274. (0.169 s) Computing T_256 on space of dimension 274. (0.13 s) T_257 sparse... (0.07 s). Computing T_258 on space of dimension 274. (0.11 s) Computing T_259 on space of dimension 274. (0.109 s) Computing T_260 on space of dimension 274. (0.15 s) Computing T_261 on space of dimension 274. (0.161 s) Computing T_262 on space of dimension 274. Computing T_131 on space of dimension 274. (3.019 s) (3.129 s) T_263 sparse... (0.07 s). Computing T_264 on space of dimension 274. (0.079 s) Computing T_265 on space of dimension 274. (0.1 s) Computing T_266 on space of dimension 274. (0.11 s) Computing T_267 on space of dimension 274. (0.17 s) Computing T_268 on space of dimension 274. (0.149 s) T_269 sparse... (0.07 s). Computing T_270 on space of dimension 274. (0.111 s) T_271 sparse... (0.07 s). Computing T_272 on space of dimension 274. (0.11 s) Computing T_273 on space of dimension 274. (0.179 s) Computing T_274 on space of dimension 274. Computing T_137 on space of dimension 274. (3.199 s) (3.309 s) Computing T_275 on space of dimension 274. (0.239 s) Computing T_276 on space of dimension 274. (0.161 s) T_277 sparse... (0.07 s). Computing T_278 on space of dimension 274. Computing T_139 on space of dimension 274. (3.219 s) (3.329 s) Computing T_279 on space of dimension 274. (0.161 s) Computing T_280 on space of dimension 274. (0.09 s) T_281 sparse... (0.07 s). Computing T_282 on space of dimension 274. (0.109 s) T_283 sparse... (0.069 s). Computing T_284 on space of dimension 274. (0.159 s) Computing T_285 on space of dimension 274. (0.17 s) Computing T_286 on space of dimension 274. (0.109 s) Computing T_287 on space of dimension 274. (0.119 s) Computing T_288 on space of dimension 274. (0.19 s) Computing T_289 on space of dimension 274. (0.159 s) Computing T_290 on space of dimension 274. (0.11 s) Computing T_291 on space of dimension 274. (0.17 s) Computing T_292 on space of dimension 274. (0.16 s) T_293 sparse... (0.07 s). Computing T_294 on space of dimension 274. (0.11 s) Computing T_295 on space of dimension 274. (0.269 s) Computing T_296 on space of dimension 274. (0.09 s) Computing T_297 on space of dimension 274. (0.24 s) Computing T_298 on space of dimension 274. Computing T_149 on space of dimension 274. (3.42 s) (3.519 s) Computing T_299 on space of dimension 274. (0.159 s) Computing T_300 on space of dimension 274. (0.16 s) Computing T_301 on space of dimension 274. (0.101 s) Computing T_302 on space of dimension 274. Computing T_151 on space of dimension 274. (3.449 s) (3.549 s) Computing T_303 on space of dimension 274. (0.17 s) Computing T_304 on space of dimension 274. (0.12 s) Computing T_305 on space of dimension 274. (0.099 s) Computing T_306 on space of dimension 274. (0.109 s) T_307 sparse... (0.07 s). Computing T_308 on space of dimension 274. (0.149 s) Computing T_309 on space of dimension 274. (0.17 s) Computing T_310 on space of dimension 274. (0.11 s) T_311 sparse... (0.079 s). Computing T_312 on space of dimension 274. (0.089 s) T_313 sparse... (0.081 s). Computing T_314 on space of dimension 274. Computing T_157 on space of dimension 274. (3.559 s) (3.669 s) Computing T_315 on space of dimension 274. (0.139 s) Computing T_316 on space of dimension 274. (0.161 s) T_317 sparse... (0.079 s). Computing T_318 on space of dimension 274. (0.099 s) Computing T_319 on space of dimension 274. (0.16 s) Computing T_320 on space of dimension 274. (0.701 s) Computing T_321 on space of dimension 274. (0.159 s) Computing T_322 on space of dimension 274. (0.1 s) Computing T_323 on space of dimension 274. (0.13 s) Computing T_324 on space of dimension 274. (0.15 s) Computing T_325 on space of dimension 274. (0.27 s) Computing T_326 on space of dimension 274. Computing T_163 on space of dimension 274. (3.661 s) (3.76 s) Computing T_327 on space of dimension 274. (0.17 s) Computing T_328 on space of dimension 274. (0.089 s) Computing T_329 on space of dimension 274. (0.141 s) Computing T_330 on space of dimension 274. (0.099 s) T_331 sparse... (0.079 s). Computing T_332 on space of dimension 274. (0.16 s) Computing T_333 on space of dimension 274. (0.141 s) Computing T_334 on space of dimension 274. Computing T_167 on space of dimension 274. (3.71 s) (3.819 s) Computing T_335 on space of dimension 274. (0.26 s) Computing T_336 on space of dimension 274. (0.15 s) T_337 sparse... (0.09 s). Computing T_338 on space of dimension 274. (0.11 s) Computing T_339 on space of dimension 274. (0.17 s) Computing T_340 on space of dimension 274. (0.17 s) Computing T_341 on space of dimension 274. (0.15 s) Computing T_342 on space of dimension 274. (0.101 s) Computing T_343 on space of dimension 274. (0.139 s) Computing T_344 on space of dimension 274. (0.099 s) Computing T_345 on space of dimension 274. (0.169 s) Computing T_346 on space of dimension 274. Computing T_173 on space of dimension 274. (3.831 s) (3.94 s) T_347 sparse... (0.081 s). Computing T_348 on space of dimension 274. (0.15 s) T_349 sparse... (0.09 s). Computing T_350 on space of dimension 274. (0.109 s) Computing T_351 on space of dimension 274. (0.23 s) Computing T_352 on space of dimension 274. (0.161 s) T_353 sparse... (0.09 s). Computing T_354 on space of dimension 274. (0.101 s) Computing T_355 on space of dimension 274. (0.259 s) Computing T_356 on space of dimension 274. (0.161 s) Computing T_357 on space of dimension 274. (0.169 s) Computing T_358 on space of dimension 274. Computing T_179 on space of dimension 274. (3.92 s) (4.019 s) T_359 sparse... (0.09 s). Computing T_360 on space of dimension 274. (0.239 s) Computing T_361 on space of dimension 274. (0.25 s) Computing T_362 on space of dimension 274. Computing T_181 on space of dimension 274. (3.929 s) (4.039 s) Computing T_363 on space of dimension 274. (0.17 s) Computing T_364 on space of dimension 274. (0.161 s) Computing T_365 on space of dimension 274. (0.279 s) Computing T_366 on space of dimension 274. (0.109 s) T_367 sparse... (0.09 s). Computing T_368 on space of dimension 274. (0.109 s) Computing T_369 on space of dimension 274. (0.15 s) Computing T_370 on space of dimension 274. (0.1 s) Computing T_371 on space of dimension 274. (0.11 s) Computing T_372 on space of dimension 274. (0.159 s) T_373 sparse... (0.099 s). Computing T_374 on space of dimension 274. (0.109 s) Computing T_375 on space of dimension 274. (0.17 s) Computing T_376 on space of dimension 274. (0.09 s) Computing T_377 on space of dimension 274. (0.169 s) Computing T_378 on space of dimension 274. (0.101 s) T_379 sparse... (0.099 s). Computing T_380 on space of dimension 274. (0.159 s) Computing T_381 on space of dimension 274. (0.179 s) Computing T_382 on space of dimension 274. Computing T_191 on space of dimension 274. (4.13 s) (4.25 s) T_383 sparse... (0.1 s). Computing T_384 on space of dimension 274. (0.67 s) Computing T_385 on space of dimension 274. (0.27 s) Computing T_386 on space of dimension 274. Computing T_193 on space of dimension 274. (4.119 s) (4.23 s) Computing T_387 on space of dimension 274. (0.13 s) Computing T_388 on space of dimension 274. (0.159 s) T_389 sparse... (0.101 s). Computing T_390 on space of dimension 274. (0.1 s) Computing T_391 on space of dimension 274. (0.121 s) Computing T_392 on space of dimension 274. (0.09 s) Computing T_393 on space of dimension 274. (0.17 s) Computing T_394 on space of dimension 274. Computing T_197 on space of dimension 274. (4.181 s) (4.29 s) Computing T_395 on space of dimension 274. (0.27 s) Computing T_396 on space of dimension 274. (0.161 s) T_397 sparse... (0.1 s). Computing T_398 on space of dimension 274. Computing T_199 on space of dimension 274. (4.25 s) (4.371 s) Computing T_399 on space of dimension 274. (0.17 s) Computing T_400 on space of dimension 274. (0.109 s) T_401 sparse... (0.24 s). Computing T_402 on space of dimension 274. (0.101 s) Computing T_403 on space of dimension 274. (0.149 s) Computing T_404 on space of dimension 274. (0.161 s) Computing T_405 on space of dimension 274. (1.019 s) Computing T_406 on space of dimension 274. (0.11 s) Computing T_407 on space of dimension 274. (0.14 s) Computing T_408 on space of dimension 274. (0.24 s) T_409 sparse... (0.099 s). Computing T_410 on space of dimension 274. (0.099 s) Computing T_411 on space of dimension 274. (0.159 s) Computing T_412 on space of dimension 274. (0.161 s) Computing T_413 on space of dimension 274. (0.37 s) Computing T_414 on space of dimension 274. (0.11 s) Computing T_415 on space of dimension 274. (0.269 s) Computing T_416 on space of dimension 274. (0.15 s) Computing T_417 on space of dimension 274. (0.169 s) Computing T_418 on space of dimension 274. (0.119 s) T_419 sparse... (0.109 s). Computing T_420 on space of dimension 274. (0.161 s) T_421 sparse... (0.11 s). Computing T_422 on space of dimension 274. Computing T_211 on space of dimension 274. (4.46 s) (4.57 s) Computing T_423 on space of dimension 274. (0.139 s) Computing T_424 on space of dimension 274. (0.09 s) Computing T_425 on space of dimension 274. (0.23 s) Computing T_426 on space of dimension 274. (0.11 s) Computing T_427 on space of dimension 274. (0.11 s) Computing T_428 on space of dimension 274. (0.16 s) Computing T_429 on space of dimension 274. (0.169 s) Computing T_430 on space of dimension 274. (0.11 s) T_431 sparse... (0.109 s). Computing T_432 on space of dimension 274. (0.121 s) T_433 sparse... (0.109 s). Computing T_434 on space of dimension 274. (0.11 s) Computing T_435 on space of dimension 274. (0.16 s) Computing T_436 on space of dimension 274. (0.161 s) Computing T_437 on space of dimension 274. (0.199 s) Computing T_438 on space of dimension 274. (0.09 s) T_439 sparse... (0.11 s). Computing T_440 on space of dimension 274. (0.239 s) Computing T_441 on space of dimension 274. (0.11 s) Computing T_442 on space of dimension 274. (0.11 s) T_443 sparse... (0.109 s). Computing T_444 on space of dimension 274. (0.161 s) Computing T_445 on space of dimension 274. (0.26 s) Computing T_446 on space of dimension 274. Computing T_223 on space of dimension 274. (4.579 s) (4.69 s) Computing T_447 on space of dimension 274. (0.17 s) Computing T_448 on space of dimension 274. (0.75 s) T_449 sparse... (0.11 s). Computing T_450 on space of dimension 274. (0.11 s) Computing T_451 on space of dimension 274. (0.139 s) Computing T_452 on space of dimension 274. (0.159 s) Computing T_453 on space of dimension 274. (0.17 s) Computing T_454 on space of dimension 274. Computing T_227 on space of dimension 274. (4.71 s) (4.819 s) Computing T_455 on space of dimension 274. (0.269 s) Computing T_456 on space of dimension 274. (0.239 s) T_457 sparse... (0.11 s). Computing T_458 on space of dimension 274. Computing T_229 on space of dimension 274. (4.721 s) (4.82 s) Computing T_459 on space of dimension 274. (0.259 s) Computing T_460 on space of dimension 274. (0.159 s) T_461 sparse... (0.11 s). Computing T_462 on space of dimension 274. (0.109 s) T_463 sparse... (0.119 s). Computing T_464 on space of dimension 274. (0.11 s) Computing T_465 on space of dimension 274. (0.17 s) Computing T_466 on space of dimension 274. Computing T_233 on space of dimension 274. (4.849 s) (4.96 s) T_467 sparse... (0.12 s). Computing T_468 on space of dimension 274. (0.161 s) Computing T_469 on space of dimension 274. (0.369 s) Computing T_470 on space of dimension 274. (0.11 s) Computing T_471 on space of dimension 274. (0.17 s) Computing T_472 on space of dimension 274. (0.24 s) Computing T_473 on space of dimension 274. (0.139 s) Computing T_474 on space of dimension 274. (0.11 s) Computing T_475 on space of dimension 274. (0.239 s) Computing T_476 on space of dimension 274. (0.15 s) Computing T_477 on space of dimension 274. (0.141 s) Computing T_478 on space of dimension 274. Computing T_239 on space of dimension 274. (4.871 s) (4.98 s) T_479 sparse... (0.119 s). Computing T_480 on space of dimension 274. (0.159 s) Computing T_481 on space of dimension 274. (0.161 s) Computing T_482 on space of dimension 274. Computing T_241 on space of dimension 274. (4.86 s) (4.969 s) Computing T_483 on space of dimension 274. (0.17 s) Computing T_484 on space of dimension 274. (0.159 s) Computing T_485 on space of dimension 274. (0.26 s) Computing T_486 on space of dimension 274. (0.109 s) T_487 sparse... (0.121 s). Computing T_488 on space of dimension 274. (0.089 s) Computing T_489 on space of dimension 274. (0.17 s) Computing T_490 on space of dimension 274. (0.1 s) T_491 sparse... (0.121 s). Computing T_492 on space of dimension 274. (0.159 s) Computing T_493 on space of dimension 274. (0.119 s) Computing T_494 on space of dimension 274. (0.119 s) Computing T_495 on space of dimension 274. (0.559 s) Computing T_496 on space of dimension 274. (0.109 s) Computing T_497 on space of dimension 274. (0.371 s) Computing T_498 on space of dimension 274. (0.099 s) T_499 sparse... (0.13 s). Computing T_500 on space of dimension 274. (0.159 s) Computing T_501 on space of dimension 274. (0.16 s) Computing T_502 on space of dimension 274. Computing T_251 on space of dimension 274. (4.971 s) (5.081 s) T_503 sparse... (0.119 s). Computing T_504 on space of dimension 274. (0.24 s) Computing T_505 on space of dimension 274. (0.269 s) Computing T_506 on space of dimension 274. (0.11 s) Computing T_507 on space of dimension 274. (0.17 s) Computing T_508 on space of dimension 274. (0.16 s) T_509 sparse... (0.13 s). Computing T_510 on space of dimension 274. (0.109 s) Computing T_511 on space of dimension 274. (0.371 s) Computing T_512 on space of dimension 274. (0.13 s) Computing T_513 on space of dimension 274. (0.259 s) Computing T_514 on space of dimension 274. Computing T_257 on space of dimension 274. (5.04 s) (5.15 s) Computing T_515 on space of dimension 274. (0.259 s) Computing T_516 on space of dimension 274. (0.159 s) Computing T_517 on space of dimension 274. (0.15 s) Computing T_518 on space of dimension 274. (0.11 s) Computing T_519 on space of dimension 274. (0.17 s) Computing T_520 on space of dimension 274. (0.239 s) T_521 sparse... (0.13 s). Computing T_522 on space of dimension 274. (0.11 s) T_523 sparse... (0.141 s). Computing T_524 on space of dimension 274. (0.129 s) Computing T_525 on space of dimension 274. (0.17 s) Computing T_526 on space of dimension 274. Computing T_263 on space of dimension 274. (5.17 s) (5.28 s) Computing T_527 on space of dimension 274. (0.11 s) Computing T_528 on space of dimension 274. (0.119 s) Computing T_529 on space of dimension 274. (0.239 s) Computing T_530 on space of dimension 274. (0.11 s) Computing T_531 on space of dimension 274. (0.54 s) Computing T_532 on space of dimension 274. (0.161 s) Computing T_533 on space of dimension 274. (0.159 s) Computing T_534 on space of dimension 274. (0.119 s) Computing T_535 on space of dimension 274. (0.27 s) Computing T_536 on space of dimension 274. (0.24 s) Computing T_537 on space of dimension 274. (0.17 s) Computing T_538 on space of dimension 274. Computing T_269 on space of dimension 274. (5.269 s) (5.391 s) Computing T_539 on space of dimension 274. (0.3 s) Computing T_540 on space of dimension 274. (0.159 s) Total time: 2588.490 seconds Magma V2.7-1 Mon Jan 29 2001 04:55:00 on modular [Seed = 577564670] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Computing space of modular symbols of level 2010 and weight 2.... I. Manin symbols list. (0.1 s) II. 2-term relations. (1.569 s) III. 3-term relations. Computing quotient by 1632 relations. Form quot and then images (1.52 s) (total time to create space = 3.229 s) Computing cuspidal part of Full Modular symbols space of level 2010, weight 2, and dimension 416 Computing new part of Modular symbols space of level 2010, weight 2, and dimension 401. Computing 2-new part of Modular symbols space of level 2010, weight 2, and dimension 401. Computing space of modular symbols of level 1005 and weight 2.... I. Manin symbols list. (0.019 s) II. 2-term relations. (0.481 s) III. 3-term relations. Computing quotient by 544 relations. Form quot and then images (0.279 s) (total time to create space = 0.79 s) Computing index-1 degeneracy map from level 2010 to 1005. (4.349 s) Computing index-2 degeneracy map from level 2010 to 1005. (4.441 s) Computing index-1 degeneracy map from level 1005 to 2010. (1.68 s) Computing index-2 degeneracy map from level 1005 to 2010. (1.07 s) Computing DualVectorSpace of Modular symbols space of level 2010, weight 2, and dimension 401. Computing complement of Modular symbols space of level 2010, weight 2, and dimension 401 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 15. Goal dimension = 15. Computing T_2 on space of dimension 416. (0.271 s) Computing T_2 on dual space of dimension 15. T_2 sparse... (0.019 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.019 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.011 s). %o x^15 - 22*x^14 + 224*x^13 - 1400*x^12 + 6006*x^11 - 18732*x^10 + 43876*x^9 - 78592*x^8 + 108545*x^7 - 115598*x^6 + 94164*x^5 - 57624*x^4 + 25648*x^3 - 7840*x^2 + 1472*x - 128 p = %o, dimension = %o. 2 82 Computing T_3 on space of dimension 416. (0.24 s) Computing T_3 on dual space of dimension 15. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^15 - 29*x^14 + 385*x^13 - 3101*x^12 + 16933*x^11 - 66353*x^10 + 192661*x^9 - 421985*x^8 + 702979*x^7 - 890967*x^6 + 852579*x^5 - 605367*x^4 + 309015*x^3 - 107163*x^2 + 22599*x - 2187 p = %o, dimension = %o. 3 33 Computing T_5 on space of dimension 416. (0.329 s) Computing T_5 on dual space of dimension 15. T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.021 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). %o x^15 - 43*x^14 + 833*x^13 - 9611*x^12 + 73605*x^11 - 395031*x^10 + 1530613*x^9 - 4352263*x^8 + 9153731*x^7 - 14257985*x^6 + 16354275*x^5 - 13610625*x^4 + 7984375*x^3 - 3128125*x^2 + 734375*x - 78125 p = %o, dimension = %o. 5 21 Computing T_7 on space of dimension 416. (0.44 s) Computing T_7 on dual space of dimension 15. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). T_7 sparse... (0.01 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). %o x^15 - 120*x^14 + 6720*x^13 - 232960*x^12 + 5591040*x^11 - 98402304*x^10 + 1312030720*x^9 - 13495173120*x^8 + 107961384960*x^7 - 671759728640*x^6 + 3224446697472*x^5 - 11725260718080*x^4 + 31267361914880*x^3 - 57724360458240*x^2 + 65970697666560*x - 35184372088832 p = %o, dimension = %o. 7 15 Computing complement of Modular symbols space of level 2010, weight 2, and dimension 15 Computing 3-new part of Modular symbols space of level 2010, weight 2, and dimension 401. Computing space of modular symbols of level 670 and weight 2.... I. Manin symbols list. (0.01 s) II. 2-term relations. (0.35 s) III. 3-term relations. Computing quotient by 408 relations. Form quot and then images (0.219 s) (total time to create space = 0.59 s) Computing index-1 degeneracy map from level 2010 to 670. (1.98 s) Computing index-3 degeneracy map from level 2010 to 670. (2.01 s) Computing index-1 degeneracy map from level 670 to 2010. (1.539 s) Computing index-3 degeneracy map from level 670 to 2010. (1.69 s) Computing 5-new part of Modular symbols space of level 2010, weight 2, and dimension 401. Computing space of modular symbols of level 402 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.25 s) III. 3-term relations. Computing quotient by 272 relations. Form quot and then images (0.121 s) (total time to create space = 0.371 s) Computing index-1 degeneracy map from level 2010 to 402. (0.849 s) Computing index-5 degeneracy map from level 2010 to 402. (0.971 s) Computing index-1 degeneracy map from level 402 to 2010. (1.589 s) Computing index-5 degeneracy map from level 402 to 2010. (2.02 s) Computing 67-new part of Modular symbols space of level 2010, weight 2, and dimension 401. Computing space of modular symbols of level 30 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.02 s) III. 3-term relations. Computing quotient by 24 relations. Form quot and then images (0.01 s) (total time to create space = 0.03 s) Computing index-1 degeneracy map from level 2010 to 30. (0.11 s) Computing index-67 degeneracy map from level 2010 to 30. (5.019 s) Computing index-1 degeneracy map from level 30 to 2010. (2.881 s) Computing index-67 degeneracy map from level 30 to 2010. (3.48 s) Finding newform decomposition of Modular symbols space of level 2010, weight 2, and dimension 401. Computing cuspidal part of Modular symbols space of level 2010, weight 2, and dimension 401 Decomposing space of level 2010 and dimension 45 using T_7. (will stop at 816) Computing T_7 on dual space of dimension 45. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.019 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.019 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.02 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.021 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.02 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.02 s). Computing characteristic polynomial of T_7. x^45 - 8*x^44 - 164*x^43 + 1440*x^42 + 11934*x^41 - 118640*x^40 - 501684*x^39 + 5935168*x^38 + 13092209*x^37 - 201673128*x^36 - 200636240*x^35 + 4932895328*x^34 + 919323816*x^33 - 89806540256*x^32 + 35603386208*x^31 + 1240951869824*x^30 - 1047411982768*x^29 - 13150535935936*x^28 + 15908642712640*x^27 + 107217304297984*x^26 - 164090568998912*x^25 - 670161418451200*x^24 + 1232001334463744*x^23 + 3174599002704896*x^22 - 6895525450692608*x^21 - 11131137501345792*x^20 + 28918263386042368*x^19 + 27531606736535552*x^18 - 90270192720871424*x^17 - 42551621268832256*x^16 + 206113733681741824*x^15 + 21858738203787264*x^14 - 333634452649410560*x^13 + 62310728664612864*x^12 + 362488078125760512*x^11 - 160759871115886592*x^10 - 237344437389230080*x^9 + 171202468640718848*x^8 + 68780784709795840*x^7 - 88605437309485056*x^6 + 7419178046717952*x^5 + 16775214545240064*x^4 - 6656031077695488*x^3 + 771857162698752*x^2 time = 0.46 Factoring characteristic polynomial. [ , , , , , , , , , , , , , , , , ] time = 0.049 Cutting out subspace using f(T_7), where f=x - 4. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.02 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Charpoly = x^2 + 10*x + 9. Decomposing space of level 2010 and dimension 2 using T_7. (will stop at 816) Computing characteristic polynomial of T_7. x^2 - 8*x + 16 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x - 4. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). Charpoly = x^2 + 22*x + 120. Decomposing space of level 2010 and dimension 2 using T_11. (will stop at 816) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.02 s). T_11 sparse... (0.01 s). Computing characteristic polynomial of T_11. x^2 - 6*x + 8 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_11), where f=x - 4. Cutting out subspace using f(T_11), where f=x - 2. Cutting out subspace using f(T_7), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Charpoly = x^2 + 12*x + 20. Decomposing space of level 2010 and dimension 2 using T_7. (will stop at 816) Computing characteristic polynomial of T_7. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.019 s). Charpoly = x^2 + 4*x. Decomposing space of level 2010 and dimension 2 using T_11. (will stop at 816) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.01 s). Computing characteristic polynomial of T_11. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_11), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.009 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Charpoly = x^2 + 4*x. Decomposing space of level 2010 and dimension 2 using T_13. (will stop at 816) Computing T_13 on dual space of dimension 2. T_13 sparse... (0.02 s). T_13 sparse... (0.01 s). Computing characteristic polynomial of T_13. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_13), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.02 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Computing T_13 on dual space of dimension 2. T_13 sparse... (0.01 s). T_13 sparse... (0.019 s). Charpoly = x^2 + 24*x + 143. Decomposing space of level 2010 and dimension 2 using T_17. (will stop at 816) Computing T_17 on dual space of dimension 2. T_17 sparse... (0.01 s). T_17 sparse... (0.009 s). Computing characteristic polynomial of T_17. x^2 + 4*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_17), where f=x. Cutting out subspace using f(T_17), where f=x + 4. Cutting out subspace using f(T_7), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Charpoly = x^2 + 4*x + 3. Decomposing space of level 2010 and dimension 2 using T_7. (will stop at 816) Computing characteristic polynomial of T_7. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). Charpoly = x^2 - 2*x - 15. Decomposing space of level 2010 and dimension 2 using T_11. (will stop at 816) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.009 s). T_11 sparse... (0.02 s). Computing characteristic polynomial of T_11. x^2 - 6*x + 8 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_11), where f=x - 4. Cutting out subspace using f(T_11), where f=x - 2. Cutting out subspace using f(T_7), where f=x + 1. Cutting out subspace using f(T_7), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). Charpoly = x^2 + 4*x - 32. Decomposing space of level 2010 and dimension 2 using T_7. (will stop at 816) Computing characteristic polynomial of T_7. x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). Charpoly = x^2 - 10*x + 9. Decomposing space of level 2010 and dimension 2 using T_11. (will stop at 816) Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.01 s). Computing characteristic polynomial of T_11. x^2 + 8*x + 16 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_11), where f=x + 4. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.02 s). Computing T_11 on dual space of dimension 2. T_11 sparse... (0.01 s). T_11 sparse... (0.009 s). Charpoly = x^2 - 20*x + 91. Decomposing space of level 2010 and dimension 2 using T_13. (will stop at 816) Computing T_13 on dual space of dimension 2. T_13 sparse... (0.02 s). T_13 sparse... (0.01 s). Computing characteristic polynomial of T_13. x^2 + 2*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_13), where f=x. Cutting out subspace using f(T_13), where f=x + 2. Cutting out subspace using f(T_7), where f=x + 3. Cutting out subspace using f(T_7), where f=x + 4. Cutting out subspace using f(T_7), where f=x^2 - x - 4. Cutting out subspace using f(T_7), where f=x^2 + 2*x - 2. Cutting out subspace using f(T_7), where f=x^3 - 3*x^2 - 12*x + 8. Cutting out subspace using f(T_7), where f=x^3 - 2*x^2 - 16*x + 16. Cutting out subspace using f(T_7), where f=x^3 - 2*x^2 - 14*x + 32. Cutting out subspace using f(T_7), where f=x^3 + x^2 - 6*x + 2. Cutting out subspace using f(T_7), where f=x^4 - x^3 - 20*x^2 + 12*x + 52. Cutting out subspace using f(T_7), where f=x^4 + 2*x^3 - 20*x^2 - 32*x + 32. Cutting out subspace using f(T_7), where f=x^5 - 5*x^4 - 18*x^3 + 114*x^2 - 72*x - 144. Cutting out subspace using f(T_7), where f=x^5 + x^4 - 20*x^3 + 8*x^2 + 44*x - 16. Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.011 s). %o x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x - 4 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 12 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). %o x - 4 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 12 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.011 s). %o x - 2 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x - 2 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.021 s). %o x p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.011 s). %o x p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x + 2 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 12 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). %o x + 2 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.01 s). %o x + 3 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.009 s). %o x - 1 p = %o, dimension = %o. 3 12 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.009 s). %o x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 1. T_7 sparse... (0.009 s). %o x + 4 p = %o, dimension = %o. 7 1 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0.02 s). %o x^2 - x - 4 p = %o, dimension = %o. 7 2 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 2. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 2. T_7 sparse... (0.02 s). T_7 sparse... (0.01 s). %o x^2 + 2*x - 2 p = %o, dimension = %o. 7 2 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.02 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 3 12 Computing T_5 on dual space of dimension 3. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 3. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). %o x^3 - 3*x^2 - 12*x + 8 p = %o, dimension = %o. 7 3 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.019 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 3. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). %o x^3 - 2*x^2 - 16*x + 16 p = %o, dimension = %o. 7 3 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.01 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 3. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). %o x^3 - 2*x^2 - 14*x + 32 p = %o, dimension = %o. 7 3 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.019 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.02 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 3. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.01 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 3. T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). %o x^3 + x^2 - 6*x + 2 p = %o, dimension = %o. 7 3 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0.02 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 4. T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 5 5 Computing T_7 on dual space of dimension 4. T_7 sparse... (0.019 s). T_7 sparse... (0.011 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). %o x^4 - x^3 - 20*x^2 + 12*x + 52 p = %o, dimension = %o. 7 4 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.02 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.01 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 4. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.011 s). T_5 sparse... (0.009 s). %o x^4 - 4*x^3 + 6*x^2 - 4*x + 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 4. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.011 s). %o x^4 + 2*x^3 - 20*x^2 - 32*x + 32 p = %o, dimension = %o. 7 4 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.011 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^5 + 5*x^4 + 10*x^3 + 10*x^2 + 5*x + 1 p = %o, dimension = %o. 2 22 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.01 s). T_3 sparse... (0.019 s). T_3 sparse... (0.009 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 3 11 Computing T_5 on dual space of dimension 5. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.009 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 5. T_7 sparse... (0.01 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). %o x^5 - 5*x^4 - 18*x^3 + 114*x^2 - 72*x - 144 p = %o, dimension = %o. 7 5 Computing representation of Modular symbols space of level 2010, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). T_2 sparse... (0.009 s). T_2 sparse... (0.01 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 2 23 Computing T_3 on dual space of dimension 5. T_3 sparse... (0.011 s). T_3 sparse... (0.009 s). T_3 sparse... (0.02 s). T_3 sparse... (0.01 s). T_3 sparse... (0.009 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 3 12 Computing T_5 on dual space of dimension 5. T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). T_5 sparse... (0.02 s). T_5 sparse... (0.01 s). T_5 sparse... (0.009 s). %o x^5 - 5*x^4 + 10*x^3 - 10*x^2 + 5*x - 1 p = %o, dimension = %o. 5 6 Computing T_7 on dual space of dimension 5. T_7 sparse... (0.02 s). T_7 sparse... (0.01 s). T_7 sparse... (0.009 s). T_7 sparse... (0.01 s). T_7 sparse... (0.019 s). %o x^5 + x^4 - 20*x^3 + 8*x^2 + 44*x - 16 p = %o, dimension = %o. 7 5 Computing cuspidal part of Full Modular symbols space of level 1005, weight 2, and dimension 140 Computing cuspidal part of Modular symbols space of level 1005, weight 2, and dimension 133 Computing new part of Modular symbols space of level 1005, weight 2, and dimension 133. Computing 3-new part of Modular symbols space of level 1005, weight 2, and dimension 133. Computing space of modular symbols of level 335 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.119 s) III. 3-term relations. Computing quotient by 136 relations. Form quot and then images (0.05 s) (total time to create space = 0.17 s) Computing index-1 degeneracy map from level 1005 to 335. (0.109 s) Computing index-3 degeneracy map from level 1005 to 335. (0.11 s) Computing index-1 degeneracy map from level 335 to 1005. (0.51 s) Computing index-3 degeneracy map from level 335 to 1005. (0.44 s) Computing DualVectorSpace of Modular symbols space of level 1005, weight 2, and dimension 133. Computing complement of Modular symbols space of level 1005, weight 2, and dimension 133 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 140. (0.029 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^7 - 21*x^6 + 189*x^5 - 945*x^4 + 2835*x^3 - 5103*x^2 + 5103*x - 2187 p = %o, dimension = %o. 2 7 Computing complement of Modular symbols space of level 1005, weight 2, and dimension 7 Computing 5-new part of Modular symbols space of level 1005, weight 2, and dimension 133. Computing space of modular symbols of level 201 and weight 2.... I. Manin symbols list. (0.011 s) II. 2-term relations. (0.079 s) III. 3-term relations. Computing quotient by 92 relations. Form quot and then images (0.029 s) (total time to create space = 0.121 s) Computing index-1 degeneracy map from level 1005 to 201. (0.07 s) Computing index-5 degeneracy map from level 1005 to 201. (0.11 s) Computing index-1 degeneracy map from level 201 to 1005. (0.49 s) Computing index-5 degeneracy map from level 201 to 1005. (0.5 s) Computing 67-new part of Modular symbols space of level 1005, weight 2, and dimension 133. Computing space of modular symbols of level 15 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.009 s) III. 3-term relations. Computing quotient by 8 relations. Form quot and then images (0 s) (total time to create space = 0.009 s) Computing index-1 degeneracy map from level 1005 to 15. (0.041 s) Computing index-67 degeneracy map from level 1005 to 15. (1.819 s) Computing index-1 degeneracy map from level 15 to 1005. (1.15 s) Computing index-67 degeneracy map from level 15 to 1005. (1.28 s) Decomposing space of level 1005 and dimension 43 using T_2. (will stop at 816) Computing T_2 on dual space of dimension 43. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing characteristic polynomial of T_2. x^43 + 3*x^42 - 59*x^41 - 177*x^40 + 1603*x^39 + 4793*x^38 - 26645*x^37 - 79015*x^36 + 303712*x^35 + 886968*x^34 - 2522864*x^33 - 7184176*x^32 + 15848630*x^31 + 43409162*x^30 - 77129554*x^29 - 199514014*x^28 + 295442108*x^27 + 704782116*x^26 - 899343496*x^25 - 1920103808*x^24 + 2184135934*x^23 + 4023779370*x^22 - 4223147250*x^21 - 6428771582*x^20 + 6445160649*x^19 + 7704940451*x^18 - 7641505011*x^17 - 6748984801*x^16 + 6874311053*x^15 + 4144283631*x^14 - 4545512319*x^13 - 1658021125*x^12 + 2120767339*x^11 + 363092185*x^10 - 661934941*x^9 - 11326007*x^8 + 127506983*x^7 - 13713499*x^6 - 12932681*x^5 + 2846645*x^4 + 406568*x^3 - 170320*x^2 + 13440*x time = 0.11 Factoring characteristic polynomial. [ , , , , , , , , , ] time = 0.049 Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x^4 - 2*x^3 - 6*x^2 + 9*x + 7. Cutting out subspace using f(T_2), where f=x^4 - 4*x^2 - x + 1. Cutting out subspace using f(T_2), where f=x^4 + 2*x^3 - 4*x^2 - 5*x + 5. Cutting out subspace using f(T_2), where f=x^4 + 4*x^3 + 2*x^2 - 5*x - 3. Cutting out subspace using f(T_2), where f=x^5 - x^4 - 6*x^3 + 5*x^2 + 4*x - 1. Cutting out subspace using f(T_2), where f=x^5 + 2*x^4 - 6*x^3 - 9*x^2 + 9*x + 4. Cutting out subspace using f(T_2), where f=x^7 - 4*x^6 - 3*x^5 + 25*x^4 - 11*x^3 - 33*x^2 + 25*x - 4. Cutting out subspace using f(T_2), where f=x^8 + 3*x^7 - 9*x^6 - 30*x^5 + 14*x^4 + 68*x^3 - 2*x^2 - 37*x + 8. Computing representation of Modular symbols space of level 1005, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 - 2*x^3 - 6*x^2 + 9*x + 7 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^4 - 4*x^2 - x + 1 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^4 + 2*x^3 - 4*x^2 - 5*x + 5 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). T_2 sparse... (0 s). %o x^4 + 4*x^3 + 2*x^2 - 5*x - 3 p = %o, dimension = %o. 2 4 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^5 - x^4 - 6*x^3 + 5*x^2 + 4*x - 1 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^5 + 2*x^4 - 6*x^3 - 9*x^2 + 9*x + 4 p = %o, dimension = %o. 2 5 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on dual space of dimension 7. T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). %o x^7 - 4*x^6 - 3*x^5 + 25*x^4 - 11*x^3 - 33*x^2 + 25*x - 4 p = %o, dimension = %o. 2 7 Computing representation of Modular symbols space of level 1005, weight 2, and dimension 8. Goal dimension = 8. Computing T_2 on dual space of dimension 8. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^8 + 3*x^7 - 9*x^6 - 30*x^5 + 14*x^4 + 68*x^3 - 2*x^2 - 37*x + 8 p = %o, dimension = %o. 2 8 Computing cuspidal part of Full Modular symbols space of level 670, weight 2, and dimension 106 Computing cuspidal part of Modular symbols space of level 670, weight 2, and dimension 99 Computing new part of Modular symbols space of level 670, weight 2, and dimension 99. Computing 2-new part of Modular symbols space of level 670, weight 2, and dimension 99. Computing index-1 degeneracy map from level 670 to 335. (0.07 s) Computing index-2 degeneracy map from level 670 to 335. (0.07 s) Computing index-1 degeneracy map from level 335 to 670. (0.339 s) Computing index-2 degeneracy map from level 335 to 670. (0.33 s) Computing DualVectorSpace of Modular symbols space of level 670, weight 2, and dimension 99. Computing complement of Modular symbols space of level 670, weight 2, and dimension 99 Computing representation of Modular symbols space of level 670, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 106. (0.019 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 23 Computing T_3 on space of dimension 106. (0.019 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^7 - 28*x^6 + 336*x^5 - 2240*x^4 + 8960*x^3 - 21504*x^2 + 28672*x - 16384 p = %o, dimension = %o. 3 7 Computing complement of Modular symbols space of level 670, weight 2, and dimension 7 Computing 5-new part of Modular symbols space of level 670, weight 2, and dimension 99. Computing space of modular symbols of level 134 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.059 s) III. 3-term relations. Computing quotient by 68 relations. Form quot and then images (0.019 s) (total time to create space = 0.079 s) Computing index-1 degeneracy map from level 670 to 134. (0.05 s) Computing index-5 degeneracy map from level 670 to 134. (0.079 s) Computing index-1 degeneracy map from level 134 to 670. (0.431 s) Computing index-5 degeneracy map from level 134 to 670. (0.389 s) Computing 67-new part of Modular symbols space of level 670, weight 2, and dimension 99. Computing space of modular symbols of level 10 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 6 relations. Form quot and then images (0.01 s) (total time to create space = 0.01 s) Computing index-1 degeneracy map from level 670 to 10. (0.019 s) Computing index-67 degeneracy map from level 670 to 10. (1.42 s) Computing index-1 degeneracy map from level 10 to 670. (0.851 s) Computing index-67 degeneracy map from level 10 to 670. (0.87 s) Decomposing space of level 670 and dimension 21 using T_3. (will stop at 816) Computing T_3 on dual space of dimension 21. T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0.001 s). T_3 sparse... (0.001 s). T_3 sparse... (0.011 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). Computing characteristic polynomial of T_3. x^21 + 4*x^20 - 32*x^19 - 144*x^18 + 368*x^17 + 2064*x^16 - 1576*x^15 - 15024*x^14 - 1696*x^13 + 58752*x^12 + 37104*x^11 - 120064*x^10 - 121392*x^9 + 111936*x^8 + 166144*x^7 - 19072*x^6 - 89664*x^5 - 24576*x^4 + 7936*x^3 + 3072*x^2 time = 0 Factoring characteristic polynomial. [ , , , , , , , ] time = 0.02 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.01 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.009 s). Charpoly = x^2 - 1. Decomposing space of level 670 and dimension 2 using T_3. (will stop at 816) Computing characteristic polynomial of T_3. x^2 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 4. Decomposing space of level 670 and dimension 2 using T_7. (will stop at 816) Computing T_7 on dual space of dimension 2. T_7 sparse... (0 s). T_7 sparse... (0 s). Computing characteristic polynomial of T_7. x^2 + 4*x - 5 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_7), where f=x - 1. Cutting out subspace using f(T_7), where f=x + 5. Cutting out subspace using f(T_3), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.01 s). Charpoly = x^2 - 4*x + 3. Decomposing space of level 670 and dimension 2 using T_3. (will stop at 816) Computing characteristic polynomial of T_3. x^2 + 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_3), where f=x + 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.009 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). Charpoly = x^2 - 12*x + 32. Decomposing space of level 670 and dimension 2 using T_7. (will stop at 816) Computing T_7 on dual space of dimension 2. T_7 sparse... (0 s). T_7 sparse... (0 s). Computing characteristic polynomial of T_7. x^2 - 1 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_7), where f=x - 1. Cutting out subspace using f(T_7), where f=x + 1. Cutting out subspace using f(T_3), where f=x^2 - 2. Cutting out subspace using f(T_3), where f=x^2 + 4*x + 2. Cutting out subspace using f(T_3), where f=x^3 - 4*x^2 + 2*x + 2. Cutting out subspace using f(T_3), where f=x^3 - 2*x^2 - 4*x + 6. Cutting out subspace using f(T_3), where f=x^3 - 6*x + 2. Cutting out subspace using f(T_3), where f=x^4 + 2*x^3 - 8*x^2 - 18*x - 8. Computing representation of Modular symbols space of level 670, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.001 s). %o x + 1 p = %o, dimension = %o. 2 11 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 670, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 1. T_3 sparse... (0.01 s). %o x p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 670, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 670, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 11 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 3 1 Computing representation of Modular symbols space of level 670, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 11 Computing T_3 on dual space of dimension 2. T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^2 - 2 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 670, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^2 + 4*x + 2 p = %o, dimension = %o. 3 2 Computing representation of Modular symbols space of level 670, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 11 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 4*x^2 + 2*x + 2 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 670, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 2*x^2 - 4*x + 6 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 670, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 10 Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^3 - 6*x + 2 p = %o, dimension = %o. 3 3 Computing representation of Modular symbols space of level 670, weight 2, and dimension 4. Goal dimension = 4. Computing T_2 on dual space of dimension 4. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^4 + 4*x^3 + 6*x^2 + 4*x + 1 p = %o, dimension = %o. 2 11 Computing T_3 on dual space of dimension 4. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.01 s). %o x^4 + 2*x^3 - 8*x^2 - 18*x - 8 p = %o, dimension = %o. 3 4 Computing cuspidal part of Full Modular symbols space of level 402, weight 2, and dimension 72 Computing cuspidal part of Modular symbols space of level 402, weight 2, and dimension 65 Computing new part of Modular symbols space of level 402, weight 2, and dimension 65. Computing 2-new part of Modular symbols space of level 402, weight 2, and dimension 65. Computing index-1 degeneracy map from level 402 to 201. (0.039 s) Computing index-2 degeneracy map from level 402 to 201. (0.029 s) Computing index-1 degeneracy map from level 201 to 402. (0.221 s) Computing index-2 degeneracy map from level 201 to 402. (0.219 s) Computing DualVectorSpace of Modular symbols space of level 402, weight 2, and dimension 65. Computing complement of Modular symbols space of level 402, weight 2, and dimension 65 Computing representation of Modular symbols space of level 402, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on space of dimension 72. (0.01 s) Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^7 - 10*x^6 + 42*x^5 - 96*x^4 + 129*x^3 - 102*x^2 + 44*x - 8 p = %o, dimension = %o. 2 19 Computing T_3 on space of dimension 72. (0.01 s) Computing T_3 on dual space of dimension 7. T_3 sparse... (0.01 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). %o x^7 - 13*x^6 + 69*x^5 - 193*x^4 + 307*x^3 - 279*x^2 + 135*x - 27 p = %o, dimension = %o. 3 10 Computing T_5 on space of dimension 72. (0.019 s) Computing T_5 on dual space of dimension 7. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). %o x^7 - 42*x^6 + 756*x^5 - 7560*x^4 + 45360*x^3 - 163296*x^2 + 326592*x - 279936 p = %o, dimension = %o. 5 7 Computing complement of Modular symbols space of level 402, weight 2, and dimension 7 Computing 3-new part of Modular symbols space of level 402, weight 2, and dimension 65. Computing index-1 degeneracy map from level 402 to 134. (0.029 s) Computing index-3 degeneracy map from level 402 to 134. (0.03 s) Computing index-1 degeneracy map from level 134 to 402. (0.201 s) Computing index-3 degeneracy map from level 134 to 402. (0.239 s) Computing 67-new part of Modular symbols space of level 402, weight 2, and dimension 65. Computing space of modular symbols of level 6 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 4 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 402 to 6. (0.02 s) Computing index-67 degeneracy map from level 402 to 6. (1.02 s) Computing index-1 degeneracy map from level 6 to 402. (0.78 s) Computing index-67 degeneracy map from level 6 to 402. (0.839 s) Decomposing space of level 402 and dimension 11 using T_5. (will stop at 816) Computing T_5 on dual space of dimension 11. T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.009 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0.01 s). T_5 sparse... (0 s). T_5 sparse... (0 s). T_5 sparse... (0 s). Computing characteristic polynomial of T_5. x^11 - 6*x^10 - 22*x^9 + 180*x^8 + 65*x^7 - 1846*x^6 + 1380*x^5 + 7144*x^4 - 9872*x^3 - 6048*x^2 + 14784*x - 5760 time = 0 Factoring characteristic polynomial. [ , , , , , ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0.001 s). T_3 sparse... (0.011 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Charpoly = x^2 - 12*x + 11. Decomposing space of level 402 and dimension 2 using T_5. (will stop at 816) Computing characteristic polynomial of T_5. x^2 - 4*x + 4 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_5), where f=x - 2. Trying to prove irreducible using random sum of Hecke operators. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.009 s). T_2 sparse... (0 s). Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0.01 s). Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). Charpoly = x^2 - 4*x. Decomposing space of level 402 and dimension 2 using T_7. (will stop at 816) Computing T_7 on dual space of dimension 2. T_7 sparse... (0.009 s). T_7 sparse... (0 s). Computing characteristic polynomial of T_7. x^2 - 2*x time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_7), where f=x - 2. Cutting out subspace using f(T_7), where f=x. Cutting out subspace using f(T_5), where f=x - 1. Cutting out subspace using f(T_5), where f=x + 3. Cutting out subspace using f(T_5), where f=x^2 - x - 10. Cutting out subspace using f(T_5), where f=x^2 - 12. Cutting out subspace using f(T_5), where f=x^3 - 3*x^2 - 4*x + 4. Computing representation of Modular symbols space of level 402, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 2 6 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 402, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0.01 s). %o x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 402, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on dual space of dimension 1. T_5 sparse... (0.01 s). %o x - 1 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 402, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 1. T_3 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 3 2 Computing T_5 on dual space of dimension 1. T_5 sparse... (0 s). %o x + 3 p = %o, dimension = %o. 5 1 Computing representation of Modular symbols space of level 402, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - 2*x + 1 p = %o, dimension = %o. 2 6 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). %o x^2 - x - 10 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 402, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 2 5 Computing T_3 on dual space of dimension 2. T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^2 + 2*x + 1 p = %o, dimension = %o. 3 3 Computing T_5 on dual space of dimension 2. T_5 sparse... (0 s). T_5 sparse... (0 s). %o x^2 - 12 p = %o, dimension = %o. 5 2 Computing representation of Modular symbols space of level 402, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 6 Computing T_3 on dual space of dimension 3. T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 3 3 Computing cuspidal part of Full Modular symbols space of level 335, weight 2, and dimension 36 Computing cuspidal part of Modular symbols space of level 335, weight 2, and dimension 33 Computing new part of Modular symbols space of level 335, weight 2, and dimension 33. Computing 5-new part of Modular symbols space of level 335, weight 2, and dimension 33. Computing space of modular symbols of level 67 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0.021 s) III. 3-term relations. Computing quotient by 24 relations. Form quot and then images (0.009 s) (total time to create space = 0.03 s) Computing index-1 degeneracy map from level 335 to 67. (0.021 s) Computing index-5 degeneracy map from level 335 to 67. (0.02 s) Computing index-1 degeneracy map from level 67 to 335. (0.11 s) Computing index-5 degeneracy map from level 67 to 335. (0.139 s) Computing DualVectorSpace of Modular symbols space of level 335, weight 2, and dimension 33. Computing complement of Modular symbols space of level 335, weight 2, and dimension 33 Computing representation of Modular symbols space of level 335, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 36. (0 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 335, weight 2, and dimension 3 Computing 67-new part of Modular symbols space of level 335, weight 2, and dimension 33. Computing space of modular symbols of level 5 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 335 to 5. (0.01 s) Computing index-67 degeneracy map from level 335 to 5. (0.599 s) Computing index-1 degeneracy map from level 5 to 335. (0.299 s) Computing index-67 degeneracy map from level 5 to 335. (0.28 s) Decomposing space of level 335 and dimension 23 using T_2. (will stop at 816) Computing T_2 on dual space of dimension 23. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^23 - 3*x^22 - 31*x^21 + 97*x^20 + 397*x^19 - 1315*x^18 - 2719*x^17 + 9745*x^16 + 10781*x^15 - 43203*x^14 - 25111*x^13 + 118093*x^12 + 33769*x^11 - 198379*x^10 - 26535*x^9 + 198389*x^8 + 15905*x^7 - 110023*x^6 - 10288*x^5 + 29260*x^4 + 4024*x^3 - 2772*x^2 - 552*x time = 0 Factoring characteristic polynomial. [ , , , , ] time = 0.02 Cutting out subspace using f(T_2), where f=x. Cutting out subspace using f(T_2), where f=x^2 - x - 1. Cutting out subspace using f(T_2), where f=x^2 - 2. Cutting out subspace using f(T_2), where f=x^7 - 2*x^6 - 12*x^5 + 21*x^4 + 42*x^3 - 52*x^2 - 39*x - 6. Cutting out subspace using f(T_2), where f=x^11 - 18*x^9 + 2*x^8 + 114*x^7 - 24*x^6 - 306*x^5 + 86*x^4 + 332*x^3 - 109*x^2 - 114*x + 46. Computing representation of Modular symbols space of level 335, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 335 to 2010. (1.51 s) Computing index-2 degeneracy map from level 335 to 2010. (1.409 s) Computing index-3 degeneracy map from level 335 to 2010. (1.5 s) Computing index-6 degeneracy map from level 335 to 2010. (1.65 s) Computing representation of Modular symbols space of level 335, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 - x - 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 335, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0.001 s). T_2 sparse... (0.011 s). %o x^2 - 2 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 335, weight 2, and dimension 7. Goal dimension = 7. Computing T_2 on dual space of dimension 7. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^7 - 2*x^6 - 12*x^5 + 21*x^4 + 42*x^3 - 52*x^2 - 39*x - 6 p = %o, dimension = %o. 2 7 Computing representation of Modular symbols space of level 335, weight 2, and dimension 11. Goal dimension = 11. Computing T_2 on dual space of dimension 11. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.009 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^11 - 18*x^9 + 2*x^8 + 114*x^7 - 24*x^6 - 306*x^5 + 86*x^4 + 332*x^3 - 109*x^2 - 114*x + 46 p = %o, dimension = %o. 2 11 Computing cuspidal part of Full Modular symbols space of level 201, weight 2, and dimension 24 Computing cuspidal part of Modular symbols space of level 201, weight 2, and dimension 21 Computing new part of Modular symbols space of level 201, weight 2, and dimension 21. Computing 3-new part of Modular symbols space of level 201, weight 2, and dimension 21. Computing index-1 degeneracy map from level 201 to 67. (0.009 s) Computing index-3 degeneracy map from level 201 to 67. (0.01 s) Computing index-1 degeneracy map from level 67 to 201. (0.07 s) Computing index-3 degeneracy map from level 67 to 201. (0.059 s) Computing DualVectorSpace of Modular symbols space of level 201, weight 2, and dimension 21. Computing complement of Modular symbols space of level 201, weight 2, and dimension 21 Computing representation of Modular symbols space of level 201, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 24. (0 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 9*x^2 + 27*x - 27 p = %o, dimension = %o. 2 3 Computing complement of Modular symbols space of level 201, weight 2, and dimension 3 Computing 67-new part of Modular symbols space of level 201, weight 2, and dimension 21. Computing space of modular symbols of level 3 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 2 relations. Form quot and then images (0 s) (total time to create space = 0 s) Computing index-1 degeneracy map from level 201 to 3. (0.009 s) Computing index-67 degeneracy map from level 201 to 3. (0.461 s) Computing index-1 degeneracy map from level 3 to 201. (0.349 s) Computing index-67 degeneracy map from level 3 to 201. (0.279 s) Decomposing space of level 201 and dimension 11 using T_2. (will stop at 816) Computing T_2 on dual space of dimension 11. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^11 - x^10 - 16*x^9 + 12*x^8 + 94*x^7 - 46*x^6 - 252*x^5 + 60*x^4 + 309*x^3 - 5*x^2 - 136*x - 20 time = 0 Factoring characteristic polynomial. [ , , , , ] time = 0.009 Cutting out subspace using f(T_2), where f=x - 1. Cutting out subspace using f(T_2), where f=x + 1. Cutting out subspace using f(T_2), where f=x + 2. Cutting out subspace using f(T_2), where f=x^3 - 3*x^2 - x + 5. Cutting out subspace using f(T_2), where f=x^5 - 8*x^3 + 13*x + 2. Computing representation of Modular symbols space of level 201, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 1 p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 201 to 2010. (1.699 s) Computing index-2 degeneracy map from level 201 to 2010. (1.65 s) Computing index-5 degeneracy map from level 201 to 2010. (1.639 s) Computing index-10 degeneracy map from level 201 to 2010. (1.73 s) Computing representation of Modular symbols space of level 201, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 1 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 201, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x + 2 p = %o, dimension = %o. 2 1 Computing representation of Modular symbols space of level 201, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 3*x^2 - x + 5 p = %o, dimension = %o. 2 3 Computing representation of Modular symbols space of level 201, weight 2, and dimension 5. Goal dimension = 5. Computing T_2 on dual space of dimension 5. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^5 - 8*x^3 + 13*x + 2 p = %o, dimension = %o. 2 5 Computing cuspidal part of Full Modular symbols space of level 134, weight 2, and dimension 19 Computing cuspidal part of Modular symbols space of level 134, weight 2, and dimension 16 Computing new part of Modular symbols space of level 134, weight 2, and dimension 16. Computing 2-new part of Modular symbols space of level 134, weight 2, and dimension 16. Computing index-1 degeneracy map from level 134 to 67. (0 s) Computing index-2 degeneracy map from level 134 to 67. (0 s) Computing index-1 degeneracy map from level 67 to 134. (0.069 s) Computing index-2 degeneracy map from level 67 to 134. (0.061 s) Computing DualVectorSpace of Modular symbols space of level 134, weight 2, and dimension 16. Computing complement of Modular symbols space of level 134, weight 2, and dimension 16 Computing representation of Modular symbols space of level 134, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on space of dimension 19. (0.001 s) Computing T_2 on dual space of dimension 3. T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). T_2 sparse... (0.001 s). %o x^3 - 4*x^2 + 5*x - 2 p = %o, dimension = %o. 2 6 Computing T_3 on space of dimension 19. (0 s) Computing T_3 on dual space of dimension 3. T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). %o x^3 - 12*x^2 + 48*x - 64 p = %o, dimension = %o. 3 3 Computing complement of Modular symbols space of level 134, weight 2, and dimension 3 Computing 67-new part of Modular symbols space of level 134, weight 2, and dimension 16. Computing space of modular symbols of level 2 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) III. 3-term relations. Computing quotient by 1 relations. Form quot and then images (0.01 s) (total time to create space = 0.01 s) Computing index-1 degeneracy map from level 134 to 2. (0 s) Computing index-67 degeneracy map from level 134 to 2. (0.399 s) Computing index-1 degeneracy map from level 2 to 134. (0.32 s) Computing index-67 degeneracy map from level 2 to 134. (0.271 s) Decomposing space of level 134 and dimension 6 using T_3. (will stop at 816) Computing T_3 on dual space of dimension 6. T_3 sparse... (0 s). T_3 sparse... (0.009 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). T_3 sparse... (0 s). Computing characteristic polynomial of T_3. x^6 - 4*x^5 - 5*x^4 + 36*x^3 - 34*x^2 - 8*x + 11 time = 0 Factoring characteristic polynomial. [ , ] time = 0 Cutting out subspace using f(T_3), where f=x^3 - 3*x^2 + 1. Cutting out subspace using f(T_3), where f=x^3 - x^2 - 8*x + 11. Computing representation of Modular symbols space of level 134, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 - 3*x^2 + 3*x - 1 p = %o, dimension = %o. 2 3 Computing index-1 degeneracy map from level 134 to 2010. (1.57 s) Computing index-3 degeneracy map from level 134 to 2010. (1.79 s) Computing index-5 degeneracy map from level 134 to 2010. (1.949 s) Computing index-15 degeneracy map from level 134 to 2010. (1.909 s) Computing representation of Modular symbols space of level 134, weight 2, and dimension 3. Goal dimension = 3. Computing T_2 on dual space of dimension 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^3 + 3*x^2 + 3*x + 1 p = %o, dimension = %o. 2 3 Computing cuspidal part of Full Modular symbols space of level 67, weight 2, and dimension 6 Computing cuspidal part of Modular symbols space of level 67, weight 2, and dimension 5 Computing new part of Modular symbols space of level 67, weight 2, and dimension 5. Computing 67-new part of Modular symbols space of level 67, weight 2, and dimension 5. Computing space of modular symbols of level 1 and weight 2.... I. Manin symbols list. (0 s) II. 2-term relations. (0 s) Decomposing space of level 67 and dimension 5 using T_2. (will stop at 816) Computing T_2 on dual space of dimension 5. Computing DualVectorSpace of Modular symbols space of level 67, weight 2, and dimension 5. Computing complement of Modular symbols space of level 67, weight 2, and dimension 5 Computing representation of Modular symbols space of level 67, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on space of dimension 6. (0 s) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 3 p = %o, dimension = %o. 2 1 Computing complement of Modular symbols space of level 67, weight 2, and dimension 1 T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x^5 + 2*x^4 - 5*x^3 - 8*x^2 + 3*x + 2 time = 0 Factoring characteristic polynomial. [ , , ] time = 0.009 Cutting out subspace using f(T_2), where f=x - 2. Cutting out subspace using f(T_2), where f=x^2 + x - 1. Cutting out subspace using f(T_2), where f=x^2 + 3*x + 1. Computing representation of Modular symbols space of level 67, weight 2, and dimension 1. Goal dimension = 1. Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). %o x - 2 p = %o, dimension = %o. 2 1 Computing index-1 degeneracy map from level 67 to 2010. (1.86 s) Computing index-2 degeneracy map from level 67 to 2010. (1.789 s) Computing index-3 degeneracy map from level 67 to 2010. (1.779 s) Computing index-5 degeneracy map from level 67 to 2010. (1.87 s) Computing index-6 degeneracy map from level 67 to 2010. (1.92 s) Computing index-10 degeneracy map from level 67 to 2010. (1.81 s) Computing index-15 degeneracy map from level 67 to 2010. (2.01 s) Computing index-30 degeneracy map from level 67 to 2010. (1.841 s) Computing representation of Modular symbols space of level 67, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 + x - 1 p = %o, dimension = %o. 2 2 Computing representation of Modular symbols space of level 67, weight 2, and dimension 2. Goal dimension = 2. Computing T_2 on dual space of dimension 2. T_2 sparse... (0 s). T_2 sparse... (0 s). %o x^2 + 3*x + 1 p = %o, dimension = %o. 2 2 Computing cuspidal part of Full Modular symbols space of level 30, weight 2, and dimension 10 Computing cuspidal part of Modular symbols space of level 30, weight 2, and dimension 3 Computing new part of Modular symbols space of level 30, weight 2, and dimension 3. Computing 2-new part of Modular symbols space of level 30, weight 2, and dimension 3. Computing index-1 degeneracy map from level 30 to 15. (0 s) Computing index-2 degeneracy map from level 30 to 15. (0.01 s) Computing index-1 degeneracy map from level 15 to 30. (0.039 s) Computing index-2 degeneracy map from level 15 to 30. (0.039 s) Computing DualVectorSpace of Modular symbols space of level 30, weight 2, and dimension 3. Goal dimension = 3. T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 3. Computing T_2 on space of dimension 10. (0 s) (0 s) %o x^3 + 2*x^2 + 3*x + 2 p = 2, dimension = 3. Computing 3-new part of Modular symbols space of level 30, weight 2, and dimension 3. Computing index-1 degeneracy map from level 30 to 10. (0.01 s) Computing index-3 degeneracy map from level 30 to 10. (0.009 s) Computing index-1 degeneracy map from level 10 to 30. (0.04 s) Computing index-3 degeneracy map from level 10 to 30. (0.03 s) Computing 5-new part of Modular symbols space of level 30, weight 2, and dimension 3. Computing index-1 degeneracy map from level 30 to 6. (0.011 s) Computing index-5 degeneracy map from level 30 to 6. (0.009 s) Computing index-1 degeneracy map from level 6 to 30. (0.05 s) Computing index-5 degeneracy map from level 6 to 30. (0.059 s) Decomposing space of level 30 and dimension 1 using T_7. (will stop at 816) Computing T_7 on dual space of dimension 1. T_7 sparse... (0 s). Computing characteristic polynomial of T_7. x + 4 time = 0.009 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_7), where f=x + 4. Computing cuspidal part of Full Modular symbols space of level 15, weight 2, and dimension 4 Computing cuspidal part of Modular symbols space of level 15, weight 2, and dimension 1 Computing new part of Modular symbols space of level 15, weight 2, and dimension 1. Computing 3-new part of Modular symbols space of level 15, weight 2, and dimension 1. Computing index-1 degeneracy map from level 15 to 5. (0 s) Computing index-3 degeneracy map from level 15 to 5. (0 s) Computing index-1 degeneracy map from level 5 to 15. (0.019 s) Computing index-3 degeneracy map from level 5 to 15. (0.009 s) Computing DualVectorSpace of Modular symbols space of level 15, weight 2, and dimension 1. Goal dimension = 1. T_2 sparse... (0 s). T_2 sparse... (0.01 s). T_2 sparse... (0 s). T_2 sparse... (0 s). Computing T_2 on space of dimension 1. Computing T_2 on space of dimension 4. (0 s) (0 s) %o x + 1 p = 2, dimension = 1. Computing 5-new part of Modular symbols space of level 15, weight 2, and dimension 1. Computing index-1 degeneracy map from level 15 to 3. (0 s) Computing index-5 degeneracy map from level 15 to 3. (0.01 s) Computing index-1 degeneracy map from level 3 to 15. (0.019 s) Computing index-5 degeneracy map from level 3 to 15. (0.019 s) Decomposing space of level 15 and dimension 1 using T_2. (will stop at 816) Computing T_2 on dual space of dimension 1. T_2 sparse... (0 s). Computing characteristic polynomial of T_2. x + 1 time = 0 Factoring characteristic polynomial. [ ] time = 0 Cutting out subspace using f(T_2), where f=x + 1. Computing index-1 degeneracy map from level 15 to 2010. (4.5 s) Computing index-2 degeneracy map from level 15 to 2010. (4.369 s) Computing index-67 degeneracy map from level 15 to 2010. (4.681 s) Computing index-134 degeneracy map from level 15 to 2010. (4.82 s) Sorting ... 17.279 seconds.