Properties

Label 235.4
Level 235
Weight 4
Dimension 5932
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 17664
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 235 = 5 \cdot 47 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(17664\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(235))\).

Total New Old
Modular forms 6808 6204 604
Cusp forms 6440 5932 508
Eisenstein series 368 272 96

Trace form

\( 5932 q - 38 q^{2} - 50 q^{3} - 62 q^{4} - 59 q^{5} - 122 q^{6} - 58 q^{7} - 46 q^{8} + O(q^{10}) \) \( 5932 q - 38 q^{2} - 50 q^{3} - 62 q^{4} - 59 q^{5} - 122 q^{6} - 58 q^{7} - 46 q^{8} - 109 q^{10} - 202 q^{11} - 78 q^{12} + 30 q^{13} + 2 q^{14} - 49 q^{15} - 10 q^{16} - 98 q^{17} - 230 q^{18} - 246 q^{19} + 11 q^{20} - 162 q^{21} + 210 q^{22} + 110 q^{23} - 46 q^{24} - 119 q^{25} - 442 q^{26} + 154 q^{27} - 142 q^{28} + 54 q^{29} - 149 q^{30} + 78 q^{31} - 558 q^{32} - 174 q^{33} + 162 q^{34} + 1969 q^{35} + 12006 q^{36} + 1446 q^{37} + 3146 q^{38} + 1486 q^{39} - 621 q^{40} - 2390 q^{41} - 7126 q^{42} - 2494 q^{43} - 7918 q^{44} - 5359 q^{45} - 9180 q^{46} - 3764 q^{47} - 20076 q^{48} - 3112 q^{49} - 2997 q^{50} - 6222 q^{51} - 2382 q^{52} - 234 q^{53} + 1914 q^{54} + 2045 q^{55} + 12006 q^{56} + 8386 q^{57} + 7466 q^{58} + 4014 q^{59} + 12603 q^{60} + 8442 q^{61} - 910 q^{62} + 230 q^{63} + 978 q^{64} - 449 q^{65} + 374 q^{66} - 298 q^{67} - 462 q^{68} + 266 q^{69} - 309 q^{70} - 962 q^{71} - 46 q^{72} + 1710 q^{73} + 2082 q^{74} - 169 q^{75} + 17858 q^{76} + 16038 q^{77} + 39918 q^{78} + 20282 q^{79} + 13620 q^{80} + 16408 q^{81} + 16276 q^{82} + 954 q^{83} - 1894 q^{84} - 3673 q^{85} - 10218 q^{86} - 9230 q^{87} - 34822 q^{88} - 13178 q^{89} - 28957 q^{90} - 39702 q^{91} - 36104 q^{92} - 16680 q^{93} - 53438 q^{94} - 15882 q^{95} - 48818 q^{96} - 15722 q^{97} - 32724 q^{98} - 27554 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(235))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
235.4.a \(\chi_{235}(1, \cdot)\) 235.4.a.a 8 1
235.4.a.b 10
235.4.a.c 13
235.4.a.d 15
235.4.c \(\chi_{235}(189, \cdot)\) 235.4.c.a 70 1
235.4.e \(\chi_{235}(93, \cdot)\) 235.4.e.a 140 2
235.4.g \(\chi_{235}(6, \cdot)\) 235.4.g.a 506 22
235.4.g.b 550
235.4.i \(\chi_{235}(4, \cdot)\) 235.4.i.a 1540 22
235.4.l \(\chi_{235}(13, \cdot)\) 235.4.l.a 3080 44

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(235))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(235)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 2}\)