Sharedwww / tables / bOpen in CoCalc
Author: William A. Stein
1
\\ b
2
\\ S_2^{new}(Gamma_0(N))
3
\\ 389<=N<=389
4
\\ E=matrix(389,?,i,j,0);
5
\\ E[N,ith eigenform found]=[[a_2,...,a_7], f(x)]
6
\\ where the a_i are defined over Q[x]/f(x).
7
\\ If p|N, a_p is replaced by the W(p) eigenvalue.
8
9
E[389,1]=[[-2,-2,-3,-5], x-1];
10
E[389,2]=[[x,x-2,-1,-2*x-1], x^2-2];
11
E[389,3]=[[x,-x,-x^2+1,-1], x^3-4*x-2];
12
E[389,4]=[[x,-20146763/1097385680*x^19+20466323/219477136*x^18+119884773/274346420*x^17-753611053/274346420*x^16-381358355/109738568*x^15+3611475535/109738568*x^14+6349339639/1097385680*x^13-56878934241/274346420*x^12+71555185319/1097385680*x^11+163330998525/219477136*x^10-223188336749/548692840*x^9-169878973265/109738568*x^8+265944624817/274346420*x^7+199655892261/109738568*x^6-1167579836501/1097385680*x^5-619178000979/548692840*x^4+261766056911/548692840*x^3+4410485304/13717321*x^2-14646077211/274346420*x-1604641167/68586605,252247073/1097385680*x^19-89195955/109738568*x^18-6876716517/1097385680*x^17+13248231811/548692840*x^16+3639338697/54869284*x^15-32041245347/109738568*x^14-367946611589/1097385680*x^13+2037515640679/1097385680*x^12+816602908511/1097385680*x^11-368120881159/54869284*x^10-19595857657/1097385680*x^9+763403091515/54869284*x^8-403904463001/137173210*x^7-1743458092745/109738568*x^6+5304122556631/1097385680*x^5+9907751136883/1097385680*x^4-704659646193/274346420*x^3-236814032039/109738568*x^2+88326575941/274346420*x+37821733103/274346420,-39775309/274346420*x^19+6458830/13717321*x^18+564024213/137173210*x^17-3911580261/274346420*x^16-2533437265/54869284*x^15+9687600453/54869284*x^14+17684386693/68586605*x^13-158547430721/137173210*x^12-196249673593/274346420*x^11+237151369759/54869284*x^10+47009341559/68586605*x^9-127672839145/13717321*x^8+263943432849/274346420*x^7+302422095641/27434642*x^6-354882792659/137173210*x^5-1763634812489/274346420*x^4+214619964123/137173210*x^3+42696419019/27434642*x^2-13851314508/68586605*x-6725054004/68586605], x^20-3*x^19-29*x^18+91*x^17+338*x^16-1130*x^15-2023*x^14+7432*x^13+6558*x^12-28021*x^11-10909*x^10+61267*x^9+6954*x^8-74752*x^7+1407*x^6+46330*x^5-1087*x^4-12558*x^3-942*x^2+960*x+148];
13
E[389,5]=[[x,x^5+3*x^4-2*x^3-8*x^2+x+2,-x^5-2*x^4+4*x^3+6*x^2-4*x-2,-2*x^5-8*x^4-2*x^3+17*x^2+7*x-6], x^6+3*x^5-2*x^4-8*x^3+2*x^2+4*x-1];
14