↑

Properties

Label 115.7
Level 115
Weight 7
Dimension 2830
Nonzero newspaces 6
Sturm bound 7392
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 115 = 5 \cdot 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(7392\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(115))\).

Total New Old
Modular forms 3256 2954 302
Cusp forms 3080 2830 250
Eisenstein series 176 124 52

Trace form

\( 2830 q - 2 q^{2} - 82 q^{3} - 22 q^{4} + 107 q^{5} + 1038 q^{6} - 1122 q^{7} - 3742 q^{8} - 22 q^{9} + O(q^{10}) \) \( 2830 q - 2 q^{2} - 82 q^{3} - 22 q^{4} + 107 q^{5} + 1038 q^{6} - 1122 q^{7} - 3742 q^{8} - 22 q^{9} + 8707 q^{10} + 2038 q^{11} - 6982 q^{12} - 3942 q^{13} - 22 q^{14} - 10325 q^{15} + 64846 q^{16} + 29418 q^{17} - 25034 q^{18} - 31702 q^{19} - 119561 q^{20} - 89562 q^{21} + 54996 q^{22} + 104812 q^{23} + 358996 q^{24} + 8863 q^{25} + 20918 q^{26} - 25702 q^{27} - 193094 q^{28} - 117062 q^{29} - 209921 q^{30} - 52522 q^{31} + 217178 q^{32} + 423970 q^{33} - 800074 q^{34} + 121407 q^{35} + 1284456 q^{36} + 599634 q^{37} + 114448 q^{38} - 128326 q^{39} - 406833 q^{40} - 43002 q^{41} - 2484922 q^{42} - 713922 q^{43} - 868912 q^{44} - 156464 q^{45} + 761686 q^{46} + 1035112 q^{47} + 2929626 q^{48} + 2282522 q^{49} + 750417 q^{50} + 1270998 q^{51} + 840918 q^{52} - 308622 q^{53} - 6438278 q^{54} - 2358769 q^{55} - 1285768 q^{56} - 549046 q^{57} + 3050648 q^{58} + 3276130 q^{59} + 1617977 q^{60} - 768490 q^{61} - 1867782 q^{62} - 2727362 q^{63} - 5947414 q^{64} - 1593049 q^{65} - 3334312 q^{66} - 286962 q^{67} - 1551604 q^{68} + 1540858 q^{69} + 2659470 q^{70} + 1553398 q^{71} + 10044296 q^{72} + 941538 q^{73} + 2076316 q^{74} - 612813 q^{75} + 7656108 q^{76} + 5489858 q^{77} + 12489118 q^{78} + 1667402 q^{79} - 773842 q^{80} + 972718 q^{81} - 12328202 q^{82} - 6922242 q^{83} - 13865346 q^{84} - 1798589 q^{85} - 5231886 q^{86} - 16842262 q^{87} - 10171110 q^{88} - 5901742 q^{89} - 6899026 q^{90} - 2263184 q^{91} + 7507608 q^{92} + 12033436 q^{93} + 13785156 q^{94} + 18330551 q^{95} + 53256072 q^{96} + 12007530 q^{97} + 10122126 q^{98} + 2254538 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(115))\)

We only show spaces with odd 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
115.7.c \(\chi_{115}(114, \cdot)\) 115.7.c.a 1 1
115.7.c.b 1
115.7.c.c 68
115.7.d \(\chi_{115}(91, \cdot)\) 115.7.d.a 48 1
115.7.f \(\chi_{115}(47, \cdot)\) n/a 132 2
115.7.h \(\chi_{115}(11, \cdot)\) n/a 480 10
115.7.i \(\chi_{115}(14, \cdot)\) n/a 700 10
115.7.k \(\chi_{115}(2, \cdot)\) n/a 1400 20

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(115))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(115)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)