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Properties

Label 95.7
Level 95
Weight 7
Dimension 1918
Nonzero newspaces 9
Newform subspaces 12
Sturm bound 5040
Trace bound 1

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 12 \)
Sturm bound: \(5040\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(95))\).

Total New Old
Modular forms 2232 2018 214
Cusp forms 2088 1918 170
Eisenstein series 144 100 44

Trace form

\( 1918 q + 2 q^{2} - 78 q^{3} - 18 q^{4} + 113 q^{5} + 1050 q^{6} - 1118 q^{7} - 3738 q^{8} - 18 q^{9} + O(q^{10}) \) \( 1918 q + 2 q^{2} - 78 q^{3} - 18 q^{4} + 113 q^{5} + 1050 q^{6} - 1118 q^{7} - 3738 q^{8} - 18 q^{9} + 8713 q^{10} + 2050 q^{11} - 6978 q^{12} + 16222 q^{13} + 7470 q^{14} - 11511 q^{15} - 74534 q^{16} - 7858 q^{17} + 1704 q^{18} + 42318 q^{19} + 23778 q^{20} + 73938 q^{21} + 119822 q^{22} + 70082 q^{23} - 186642 q^{24} - 139451 q^{25} - 241406 q^{26} - 312318 q^{27} + 363416 q^{28} + 231822 q^{29} + 444792 q^{30} + 127850 q^{31} - 126148 q^{32} - 654090 q^{33} - 627768 q^{34} - 175519 q^{35} - 593634 q^{36} - 293756 q^{37} + 308748 q^{38} + 854244 q^{39} + 871098 q^{40} + 813010 q^{41} + 1608642 q^{42} + 32194 q^{43} - 1039068 q^{44} - 423207 q^{45} - 785140 q^{46} + 207482 q^{47} - 888552 q^{48} - 123138 q^{49} + 510812 q^{50} + 417990 q^{51} - 2314538 q^{52} - 1366378 q^{53} - 1719540 q^{54} - 1260163 q^{55} - 934632 q^{56} + 660942 q^{57} + 2431164 q^{58} + 2267982 q^{59} - 121464 q^{60} + 795530 q^{61} + 5876452 q^{62} + 5887122 q^{63} + 6410430 q^{64} + 1869833 q^{65} - 1608006 q^{66} - 2175470 q^{67} - 11043788 q^{68} - 7543170 q^{69} - 5117943 q^{70} - 4244030 q^{71} - 5929380 q^{72} - 4371398 q^{73} - 2324322 q^{74} + 870864 q^{75} + 5138286 q^{76} + 10680700 q^{77} + 12359466 q^{78} + 8410158 q^{79} - 5258995 q^{80} + 4208526 q^{81} + 1713176 q^{82} - 1938334 q^{83} - 4255866 q^{84} + 1692325 q^{85} - 6225812 q^{86} - 1876722 q^{87} - 1225218 q^{88} - 7304922 q^{89} + 11703408 q^{90} - 1895662 q^{91} + 15917240 q^{92} + 14020206 q^{93} - 8862291 q^{95} - 14384316 q^{96} + 2509510 q^{97} + 16681216 q^{98} + 2789730 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.7.c \(\chi_{95}(56, \cdot)\) 95.7.c.a 40 1
95.7.d \(\chi_{95}(94, \cdot)\) 95.7.d.a 2 1
95.7.d.b 4
95.7.d.c 4
95.7.d.d 48
95.7.f \(\chi_{95}(58, \cdot)\) 95.7.f.a 108 2
95.7.h \(\chi_{95}(69, \cdot)\) 95.7.h.a 116 2
95.7.j \(\chi_{95}(31, \cdot)\) 95.7.j.a 80 2
95.7.m \(\chi_{95}(7, \cdot)\) 95.7.m.a 232 4
95.7.n \(\chi_{95}(21, \cdot)\) 95.7.n.a 240 6
95.7.o \(\chi_{95}(14, \cdot)\) 95.7.o.a 348 6
95.7.q \(\chi_{95}(17, \cdot)\) 95.7.q.a 696 12

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)