↑

Properties

Label 656.6
Level 656
Weight 6
Dimension 37580
Nonzero newspaces 20
Sturm bound 161280
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 656 = 2^{4} \cdot 41 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(161280\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(656))\).

Total New Old
Modular forms 67760 37930 29830
Cusp forms 66640 37580 29060
Eisenstein series 1120 350 770

Trace form

\( 37580 q - 76 q^{2} - 40 q^{3} - 32 q^{4} - 56 q^{5} - 304 q^{6} - 284 q^{7} - 568 q^{8} - 136 q^{9} + O(q^{10}) \) \( 37580 q - 76 q^{2} - 40 q^{3} - 32 q^{4} - 56 q^{5} - 304 q^{6} - 284 q^{7} - 568 q^{8} - 136 q^{9} + 792 q^{10} + 2480 q^{11} - 88 q^{12} - 216 q^{13} + 120 q^{14} - 7908 q^{15} + 1664 q^{16} + 1036 q^{17} + 6196 q^{18} + 12424 q^{19} - 6024 q^{20} - 2220 q^{21} - 8920 q^{22} - 7900 q^{23} - 16816 q^{24} - 4304 q^{25} - 14816 q^{26} - 3724 q^{27} + 14592 q^{28} - 488 q^{29} + 60808 q^{30} + 20068 q^{31} + 47904 q^{32} + 7828 q^{33} + 3400 q^{34} - 23284 q^{35} - 13864 q^{36} + 1144 q^{37} - 106576 q^{38} + 29092 q^{39} - 150624 q^{40} - 8360 q^{41} - 66960 q^{42} - 11872 q^{43} + 80168 q^{44} + 22304 q^{45} + 184984 q^{46} - 43676 q^{47} + 295904 q^{48} + 79228 q^{49} + 170020 q^{50} - 56740 q^{51} - 183224 q^{52} - 111912 q^{53} - 417424 q^{54} + 39908 q^{55} - 382336 q^{56} - 101716 q^{57} - 213632 q^{58} + 77824 q^{59} + 308656 q^{60} + 202504 q^{61} + 547664 q^{62} + 34140 q^{63} + 567472 q^{64} + 60340 q^{65} + 306632 q^{66} + 162920 q^{67} - 267504 q^{68} - 151564 q^{69} - 824400 q^{70} - 157724 q^{71} - 940568 q^{72} - 125372 q^{73} - 294376 q^{74} - 210456 q^{75} + 174856 q^{76} + 18772 q^{77} + 1263480 q^{78} + 40964 q^{79} + 1108832 q^{80} + 221536 q^{81} + 93136 q^{82} - 185636 q^{83} - 381856 q^{84} + 35748 q^{85} - 941016 q^{86} - 117084 q^{87} - 1180736 q^{88} - 203516 q^{89} - 560384 q^{90} + 512892 q^{91} + 443712 q^{92} - 30212 q^{93} + 921744 q^{94} + 140476 q^{95} + 1194576 q^{96} + 146892 q^{97} + 889212 q^{98} + 525496 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(656))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
656.6.a \(\chi_{656}(1, \cdot)\) 656.6.a.a 3 1
656.6.a.b 4
656.6.a.c 5
656.6.a.d 6
656.6.a.e 6
656.6.a.f 6
656.6.a.g 10
656.6.a.h 10
656.6.a.i 11
656.6.a.j 12
656.6.a.k 13
656.6.a.l 14
656.6.b \(\chi_{656}(329, \cdot)\) None 0 1
656.6.d \(\chi_{656}(81, \cdot)\) n/a 104 1
656.6.g \(\chi_{656}(409, \cdot)\) None 0 1
656.6.i \(\chi_{656}(173, \cdot)\) n/a 836 2
656.6.l \(\chi_{656}(337, \cdot)\) n/a 208 2
656.6.n \(\chi_{656}(165, \cdot)\) n/a 800 2
656.6.o \(\chi_{656}(245, \cdot)\) n/a 836 2
656.6.r \(\chi_{656}(9, \cdot)\) None 0 2
656.6.t \(\chi_{656}(237, \cdot)\) n/a 836 2
656.6.u \(\chi_{656}(305, \cdot)\) n/a 416 4
656.6.v \(\chi_{656}(331, \cdot)\) n/a 1672 4
656.6.z \(\chi_{656}(55, \cdot)\) None 0 4
656.6.ba \(\chi_{656}(79, \cdot)\) n/a 420 4
656.6.bb \(\chi_{656}(3, \cdot)\) n/a 1672 4
656.6.be \(\chi_{656}(113, \cdot)\) n/a 416 4
656.6.bg \(\chi_{656}(57, \cdot)\) None 0 4
656.6.bi \(\chi_{656}(25, \cdot)\) None 0 4
656.6.bl \(\chi_{656}(197, \cdot)\) n/a 3344 8
656.6.bm \(\chi_{656}(121, \cdot)\) None 0 8
656.6.bp \(\chi_{656}(45, \cdot)\) n/a 3344 8
656.6.bq \(\chi_{656}(37, \cdot)\) n/a 3344 8
656.6.bs \(\chi_{656}(33, \cdot)\) n/a 832 8
656.6.bu \(\chi_{656}(5, \cdot)\) n/a 3344 8
656.6.bx \(\chi_{656}(259, \cdot)\) n/a 6688 16
656.6.by \(\chi_{656}(15, \cdot)\) n/a 1680 16
656.6.bz \(\chi_{656}(7, \cdot)\) None 0 16
656.6.cd \(\chi_{656}(11, \cdot)\) n/a 6688 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(656))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(656)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 1}\)