CoCalc -- Collaborative Calculation in the Cloud
Sharedwww / Tables / slopes_3-adic.mOpen in CoCalc
/*********************************************************************
 This is a MAGMA-readable table of the 3-adic slopes of the Hecke 
 operator T_3 acting on Gamma_0(N).  The syntax is:
     <N,
      [
      <k, [* slopes of T_3 on S_k(Gamma_0(N)) *]
      ...
      ]>

 William Stein, February 13, 2000
***********************************************************************/

oo := Infinity();

slopes_3adic :=
[*
<1,
[ 
<2, [**]>,
<4, [**]>,
<6, [**]>,
<8, [**]>,
<10, [**]>,
<12, [* 2 *]>,
<14, [**]>,
<16, [* 3 *]>,
<18, [* 2 *]>,
<20, [* 3 *]>,
<22, [* 3 *]>,
<24, [* 2, 5 *]>,
<26, [* 3 *]>,
<28, [* 4, 4 *]>,
<30, [* 2, 5 *]>,
<32, [* 4, 6 *]>,
<34, [* 3, 6 *]>,
<36, [* 2, 6, 8 *]>,
<38, [* 3, 7 *]>,
<40, [* 3, 6, 9 *]>,
<42, [* 2, 5, 9 *]>,
<44, [* 3, 7, 9 *]>,
<46, [* 4, 4, 9 *]>,
<48, [* 2, 5, 9, 11 *]>,
<50, [* 4, 6, 8 *]>,
<52, [* 3, 6, 8, 12 *]>,
<54, [* 2, 6, 8, 10 *]>,
<56, [* 3, 7, 9, 11 *]>,
<58, [* 3, 6, 9, 11 *]>,
<60, [* 2, 5, 9, 11, 13 *]>,
<62, [* 3, 7, 9, 12 *]>,
<64, [* 4, 4, 9, 13, 13 *]>,
<66, [* 2, 5, 9, 11, 14 *]>,
<68, [* 5, 6, 7, 13, 15 *]>,
<70, [* 3, 7, 7, 12, 15 *]>,
<72, [* 2, 7, 8, 9, 15, 17 *]>,
<74, [* 3, 8, 9, 10, 16 *]>,
<76, [* 3, 7, 10, 10, 13, 18 *]>,
<78, [* 2, 5, 10, 11, 12, 18 *]>,
<80, [* 3, 8, 10, 12, 14, 16 *]>,
<82, [* 4, 4, 10, 13, 13, 16 *]>,
<84, [* 2, 5, 10, 12, 14, 16, 18 *]>,
<86, [* 4, 6, 9, 14, 15, 16 *]>,
<88, [* 3, 6, 9, 13, 16, 16, 19 *]>,
<90, [* 2, 6, 8, 11, 16, 17, 18 *]>,
<92, [* 3, 7, 10, 12, 17, 18, 19 *]>,
<94, [* 3, 6, 9, 12, 15, 19, 19 *]>,
<96, [* 2, 5, 9, 12, 14, 19, 20, 21 *]>,
<98, [* 3, 7, 9, 13, 16, 18, 21 *]>,
<100, [* 4, 4, 9, 14, 14, 18, 22, 22 *]>,
<102, [* 2, 5, 9, 11, 15, 18, 20, 23 *]>,
<104, [* 4, 6, 8, 14, 16, 18, 22, 24 *]>,
<106, [* 3, 6, 8, 12, 16, 18, 21, 24 *]>,
<108, [* 2, 6, 8, 10, 16, 18, 20, 24, 26 *]>,
<110, [* 3, 7, 9, 11, 17, 19, 21, 25 *]>,
<112, [* 3, 6, 9, 11, 15, 19, 21, 24, 27 *]>,
<114, [* 2, 5, 9, 11, 13, 19, 21, 23, 27 *]>,
<116, [* 3, 7, 9, 12, 16, 18, 22, 25, 27 *]>,
<118, [* 4, 4, 9, 13, 13, 18, 23, 23, 27 *]>,
<120, [* 2, 5, 9, 11, 14, 18, 20, 24, 27, 29 *]>,
<122, [* 5, 6, 7, 13, 15, 18, 22, 25, 27 *]>,
<124, [* 3, 7, 7, 12, 15, 18, 21, 24, 27, 30 *]>,
<126, [* 2, 7, 8, 9, 15, 17, 20, 24, 27, 29 *]>,
<128, [* 3, 8, 9, 10, 16, 19, 21, 25, 27, 30 *]>,
<130, [* 3, 7, 10, 10, 13, 18, 21, 24, 27, 30 *]>,
<132, [* 2, 5, 10, 11, 12, 18, 21, 23, 27, 29, 32 *]>,
<134, [* 3, 8, 10, 12, 14, 16, 22, 25, 27, 30 *]>,
<136, [* 4, 4, 10, 13, 13, 16, 23, 23, 27, 31, 31 *]>,
<138, [* 2, 5, 10, 12, 14, 16, 18, 24, 27, 29, 32 *]>,
<140, [* 4, 6, 9, 14, 15, 16, 21, 25, 27, 31, 33 *]>,
<142, [* 3, 6, 9, 13, 16, 16, 19, 23, 27, 30, 33 *]>,
<144, [* 2, 6, 8, 11, 16, 17, 18, 23, 27, 29, 33, 35 *]>,
<146, [* 3, 7, 10, 12, 17, 18, 19, 24, 26, 30, 34 *]>,
<148, [* 3, 6, 9, 12, 15, 19, 19, 23, 26, 30, 33, 36 *]>,
<150, [* 2, 5, 9, 12, 14, 19, 20, 21, 26, 28, 32, 36 *]>
]>,

<2,[ 
<2, [**]>,
<4, [**]>,
<6, [**]>,
<8, [* 1 *]>,
<10, [* 1 *]>,
<12, [* 2, 2 *]>,
<14, [* 1, 3 *]>,
<16, [* 1, 3, 3 *]>,
<18, [* 2, 2, 2 *]>,
<20, [* 1, 3, 3, 3 *]>,
<22, [* 1, 3, 3, 4 *]>,
<24, [* 2, 2, 2, 5, 5 *]>,
<26, [* 1, 3, 3, 3, 6 *]>,
<28, [* 1, 4, 4, 4, 4, 4 *]>,
<30, [* 2, 2, 3, 5, 5, 5 *]>,
<32, [* 1, 3, 4, 4, 6, 6, 6 *]>,
<34, [* 1, 3, 3, 5, 6, 6, 7 *]>,
<36, [* 2, 2, 2, 6, 6, 6, 8, 8 *]>,
<38, [* 1, 3, 3, 3, 7, 7, 7, 9 *]>,
<40, [* 1, 3, 3, 4, 6, 6, 8, 9, 9 *]>,
<42, [* 2, 2, 2, 5, 5, 6, 8, 9, 9 *]>,
<44, [* 1, 3, 3, 3, 6, 7, 7, 9, 9, 10 *]>,
<46, [* 1, 4, 4, 4, 4, 4, 8, 9, 9, 10 *]>,
<48, [* 2, 2, 3, 5, 5, 5, 7, 9, 9, 11, 11 *]>,
<50, [* 1, 3, 4, 4, 6, 6, 6, 8, 8, 10, 12 *]> 
]>,

<3,[
<2, [**]>,
<4, [**]>,
<6, [* 2 *]>,
<8, [* 3 *]>,
<10, [* 4, 4 *]>,
<12, [* 2, 5, 9 *]>,
<14, [* 6, 6, 6 *]>,
<16, [* 3, 7, 7, 12 *]>,
<18, [* 2, 8, 8, 8, 15 *]>,
<20, [* 3, 9, 9, 9, 16 *]>,
<22, [* 3, 10, 10, 10, 10, 18 *]>,
<24, [* 2, 5, 11, 11, 11, 18, 21 *]>,
<26, [* 3, 12, 12, 12, 12, 12, 22 *]>,
<28, [* 4, 4, 13, 13, 13, 13, 23, 23 *]>,
<30, [* 2, 5, 14, 14, 14, 14, 14, 24, 27 *]>,
<32, [* 4, 6, 15, 15, 15, 15, 15, 25, 27 *]>,
<34, [* 3, 6, 16, 16, 16, 16, 16, 16, 27, 30 *]>,
<36, [* 2, 6, 8, 17, 17, 17, 17, 17, 27, 29, 33 *]>,
<38, [* 3, 7, 18, 18, 18, 18, 18, 18, 18, 30, 34 *]>,
<40, [* 3, 6, 9, 19, 19, 19, 19, 19, 19, 30, 33, 36 *]>,
<42, [* 2, 5, 9, 20, 20, 20, 20, 20, 20, 20, 32, 36, 39 *]>,
<44, [* 3, 7, 9, 21, 21, 21, 21, 21, 21, 21, 34, 36, 40 *]>,
<46, [* 4, 4, 9, 22, 22, 22, 22, 22, 22, 22, 22, 36, 41, 41 *]>,
<48, [* 2, 5, 9, 11, 23, 23, 23, 23, 23, 23, 23, 36, 38, 42, 45 *]>,
<50, [* 4, 6, 8, 24, 24, 24, 24, 24, 24, 24, 24, 24, 41, 43, 45 *]>
]>,

<6,[ 
<2, [**]>,
<4, [* 1 *]>,
<6, [* 2, 2, 2 *]>,
<8, [* 1, 3, 3, 3, 6 *]>,
<10, [* 1, 4, 4, 4, 4, 4, 8 *]>,
<12, [* 2, 2, 5, 5, 5, 5, 5, 9, 9 *]>,
<14, [* 1, 3, 6, 6, 6, 6, 6, 6, 6, 10, 12 *]>,
<16, [* 1, 3, 3, 7, 7, 7, 7, 7, 7, 7, 12, 12, 14 *]>,
<18, [* 2, 2, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 15, 15, 15 *]>,
<20, [* 1, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 16, 16, 16, 18 *]>,
<22, [* 1, 3, 3, 4, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 17, 18, 18, 20 *]>,
<24, [* 2, 2, 2, 5, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 18, 18, 21, 21, 21 *]>,
<26, [* 1, 3, 3, 3, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 19, 22, 22, 22, 24 *]>,
<28, [* 1, 4, 4, 4, 4, 4, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 23, 23, 23, 23, 23, 26 *]>,
<30, [* 2, 2, 3, 5, 5, 5, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 24, 24, 24, 26, 27, 27 *]>,
<32, [* 1, 3, 4, 4, 6, 6, 6, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 25, 25, 25, 27, 27, 28, 30 *]>,
<34, [* 1, 3, 3, 5, 6, 6, 7, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 26, 27, 27, 28, 30, 30, 32 *]>,
<36, [* 2, 2, 2, 6, 6, 6, 8, 8, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 27, 27, 29, 29, 29, 33, 33, 33 *]>,
<38, [* 1, 3, 3, 3, 7, 7, 7, 9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 28, 30, 30, 30, 34, 34, 34, 36 *]>,
<40, [* 1, 3, 3, 4, 6, 6, 8, 9, 9, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 30, 30, 31, 33, 33, 35, 36, 36, 38 *]>,
<42, [* 2, 2, 2, 5, 5, 6, 8, 9, 9, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 32, 32, 33, 35, 36,
36, 39, 39, 39 *]>,
<44, [* 1, 3, 3, 3, 6, 7, 7, 9, 9, 10, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 33, 34, 34, 36, 36, 37, 40, 40, 40, 42 *]>,
<46, [* 1, 4, 4, 4, 4, 4, 8, 9, 9, 10, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 35, 36, 36, 37, 41, 41, 41, 41, 41, 44 *]>,
<48, [* 2, 2, 3, 5, 5, 5, 7, 9, 9, 11, 11, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 36, 36, 38, 38, 40, 42, 42, 42, 44, 45, 45 *]>,
<50, [* 1, 3, 4, 4, 6, 6, 6, 8, 8, 10, 12, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 37, 39, 41,
41, 43, 43, 43, 45, 45, 46, 48 *]>
]>,

<9,[ 
<2, [**]>,
<4, [* oo *]>,
<6, [* 2, oo, oo *]>,
<8, [* 3, oo, oo, oo, oo *]>,
<10, [* 4, 4, oo, oo, oo, oo, oo *]>,
<12, [* 2, 5, 9, oo, oo, oo, oo, oo, oo *]>,
<14, [* 6, 6, 6, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<16, [* 3, 7, 7, 12, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<18, [* 2, 8, 8, 8, 15, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<20, [* 3, 9, 9, 9, 16, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<22, [* 3, 10, 10, 10, 10, 18, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<24, [* 2, 5, 11, 11, 11, 18, 21, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>, 
<26, [* 3, 12, 12, 12, 12, 12, 22, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<28, [* 4, 4, 13, 13, 13, 13, 23, 23, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<30, [* 2, 5, 14, 14, 14, 14, 14, 24, 27, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<32, [* 4, 6, 15, 15, 15, 15, 15, 25, 27, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<34, [* 3, 6, 16, 16, 16, 16, 16, 16, 27, 30, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<36, [* 2, 6, 8, 17, 17, 17, 17, 17, 27, 29, 33, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<38, [* 3, 7, 18, 18, 18, 18, 18, 18, 18, 30, 34, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<40, [* 3, 6, 9, 19, 19, 19, 19, 19, 19, 30, 33, 36, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<42, [* 2, 5, 9, 20, 20, 20, 20, 20, 20, 20, 32, 36, 39, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<44, [* 3, 7, 9, 21, 21, 21, 21, 21, 21, 21, 34, 36, 40, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo,
oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<46, [* 4, 4, 9, 22, 22, 22, 22, 22, 22, 22, 22, 36, 41, 41, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<48, [* 2, 5, 9, 11, 23, 23, 23, 23, 23, 23, 23, 36, 38, 42, 45, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>,
<50, [* 4, 6, 8, 24, 24, 24, 24, 24, 24, 24, 24, 24, 41, 43, 45, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo, oo *]>
]>


*];