↑

Properties

Label 637.4
Level 637
Weight 4
Dimension 46299
Nonzero newspaces 30
Sturm bound 131712
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(131712\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(637))\).

Total New Old
Modular forms 50112 47365 2747
Cusp forms 48672 46299 2373
Eisenstein series 1440 1066 374

Trace form

\( 46299 q - 156 q^{2} - 180 q^{3} - 156 q^{4} - 108 q^{5} - 24 q^{6} - 132 q^{7} - 456 q^{8} - 324 q^{9} + O(q^{10}) \) \( 46299 q - 156 q^{2} - 180 q^{3} - 156 q^{4} - 108 q^{5} - 24 q^{6} - 132 q^{7} - 456 q^{8} - 324 q^{9} - 174 q^{10} - 96 q^{11} + 258 q^{12} - 21 q^{13} - 348 q^{14} + 84 q^{15} + 84 q^{16} - 33 q^{17} - 1056 q^{18} - 1224 q^{19} - 1332 q^{20} - 636 q^{21} + 90 q^{22} + 912 q^{23} + 1464 q^{24} + 1053 q^{25} + 585 q^{26} + 618 q^{27} + 204 q^{28} - 657 q^{29} - 984 q^{30} - 996 q^{31} - 2082 q^{32} - 540 q^{33} - 1392 q^{34} - 300 q^{35} + 3420 q^{36} + 2883 q^{37} + 6474 q^{38} + 2049 q^{39} + 7134 q^{40} + 3585 q^{41} - 426 q^{42} - 2664 q^{43} - 6822 q^{44} - 9507 q^{45} - 8820 q^{46} - 4680 q^{47} - 16494 q^{48} - 7944 q^{49} - 10026 q^{50} - 7434 q^{51} - 6543 q^{52} - 3594 q^{53} - 4074 q^{54} - 792 q^{55} + 288 q^{56} + 6552 q^{57} + 7914 q^{58} + 9216 q^{59} + 23862 q^{60} + 9009 q^{61} + 10800 q^{62} + 9528 q^{63} + 7194 q^{64} - 3132 q^{65} - 4254 q^{66} - 1740 q^{67} - 666 q^{68} - 7404 q^{69} - 930 q^{70} - 4836 q^{71} + 19086 q^{72} + 8844 q^{73} + 27870 q^{74} + 26754 q^{75} + 45612 q^{76} + 10224 q^{77} + 24879 q^{78} + 12978 q^{79} + 44172 q^{80} + 34758 q^{81} + 19548 q^{82} + 18456 q^{83} + 22380 q^{84} - 12963 q^{85} - 12336 q^{86} - 34116 q^{87} - 77352 q^{88} - 29172 q^{89} - 100584 q^{90} - 19443 q^{91} - 72024 q^{92} - 73560 q^{93} - 95646 q^{94} - 61248 q^{95} - 121116 q^{96} - 41202 q^{97} - 60048 q^{98} - 35106 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(637))\)

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
637.4.a \(\chi_{637}(1, \cdot)\) 637.4.a.a 1 1
637.4.a.b 2
637.4.a.c 3
637.4.a.d 4
637.4.a.e 5
637.4.a.f 6
637.4.a.g 9
637.4.a.h 9
637.4.a.i 11
637.4.a.j 11
637.4.a.k 13
637.4.a.l 13
637.4.a.m 18
637.4.a.n 18
637.4.c \(\chi_{637}(246, \cdot)\) n/a 138 1
637.4.e \(\chi_{637}(79, \cdot)\) n/a 240 2
637.4.f \(\chi_{637}(295, \cdot)\) n/a 278 2
637.4.g \(\chi_{637}(263, \cdot)\) n/a 272 2
637.4.h \(\chi_{637}(165, \cdot)\) n/a 272 2
637.4.i \(\chi_{637}(489, \cdot)\) n/a 272 2
637.4.k \(\chi_{637}(459, \cdot)\) n/a 272 2
637.4.q \(\chi_{637}(491, \cdot)\) n/a 276 2
637.4.r \(\chi_{637}(116, \cdot)\) n/a 272 2
637.4.u \(\chi_{637}(30, \cdot)\) n/a 272 2
637.4.w \(\chi_{637}(92, \cdot)\) n/a 1008 6
637.4.x \(\chi_{637}(19, \cdot)\) n/a 544 4
637.4.bb \(\chi_{637}(227, \cdot)\) n/a 544 4
637.4.bc \(\chi_{637}(31, \cdot)\) n/a 544 4
637.4.bd \(\chi_{637}(97, \cdot)\) n/a 544 4
637.4.bg \(\chi_{637}(64, \cdot)\) n/a 1164 6
637.4.bi \(\chi_{637}(16, \cdot)\) n/a 2328 12
637.4.bj \(\chi_{637}(9, \cdot)\) n/a 2328 12
637.4.bk \(\chi_{637}(22, \cdot)\) n/a 2328 12
637.4.bl \(\chi_{637}(53, \cdot)\) n/a 2016 12
637.4.bn \(\chi_{637}(34, \cdot)\) n/a 2328 12
637.4.bp \(\chi_{637}(88, \cdot)\) n/a 2328 12
637.4.bs \(\chi_{637}(25, \cdot)\) n/a 2328 12
637.4.bt \(\chi_{637}(36, \cdot)\) n/a 2328 12
637.4.bz \(\chi_{637}(4, \cdot)\) n/a 2328 12
637.4.cb \(\chi_{637}(6, \cdot)\) n/a 4656 24
637.4.cc \(\chi_{637}(5, \cdot)\) n/a 4656 24
637.4.cd \(\chi_{637}(45, \cdot)\) n/a 4656 24
637.4.ch \(\chi_{637}(24, \cdot)\) n/a 4656 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(637))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(637)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 2}\)