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Properties

Label 95.4
Level 95
Weight 4
Dimension 934
Nonzero newspaces 9
Newform subspaces 20
Sturm bound 2880
Trace bound 4

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 20 \)
Sturm bound: \(2880\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(95))\).

Total New Old
Modular forms 1152 1038 114
Cusp forms 1008 934 74
Eisenstein series 144 104 40

Trace form

\( 934 q - 10 q^{2} - 22 q^{3} - 34 q^{4} - 17 q^{5} - 38 q^{6} - 30 q^{7} - 18 q^{8} + 28 q^{9} + O(q^{10}) \) \( 934 q - 10 q^{2} - 22 q^{3} - 34 q^{4} - 17 q^{5} - 38 q^{6} - 30 q^{7} - 18 q^{8} + 28 q^{9} - 67 q^{10} - 118 q^{11} + 526 q^{12} + 346 q^{13} + 102 q^{14} - 115 q^{15} - 790 q^{16} - 358 q^{17} - 1156 q^{18} - 874 q^{19} - 550 q^{20} - 582 q^{21} - 86 q^{22} + 174 q^{23} + 846 q^{24} + 355 q^{25} + 1010 q^{26} + 2792 q^{27} + 4476 q^{28} + 1342 q^{29} + 1090 q^{30} + 342 q^{31} - 1160 q^{32} - 1982 q^{33} - 2060 q^{34} - 1083 q^{35} - 5842 q^{36} - 1864 q^{37} - 4280 q^{38} - 3664 q^{39} - 1908 q^{40} - 998 q^{41} - 2982 q^{42} - 650 q^{43} + 5320 q^{44} + 2821 q^{45} + 6360 q^{46} + 4754 q^{47} + 11452 q^{48} + 4016 q^{49} + 2378 q^{50} + 112 q^{51} - 4162 q^{52} - 3190 q^{53} - 5732 q^{54} - 1651 q^{55} - 12132 q^{56} - 5258 q^{57} - 4324 q^{58} - 5518 q^{59} - 1406 q^{60} + 6490 q^{61} + 5940 q^{62} + 7026 q^{63} + 9214 q^{64} + 2203 q^{65} + 7514 q^{66} + 1566 q^{67} + 6748 q^{68} + 942 q^{69} - 591 q^{70} + 3478 q^{71} - 8244 q^{72} - 8144 q^{73} - 8258 q^{74} - 1918 q^{75} - 14354 q^{76} - 17376 q^{77} - 25718 q^{78} - 17058 q^{79} - 22843 q^{80} - 14522 q^{81} - 13216 q^{82} - 4002 q^{83} - 4314 q^{84} + 1745 q^{85} + 9476 q^{86} + 13862 q^{87} + 21006 q^{88} + 15294 q^{89} + 31718 q^{90} + 22146 q^{91} + 31632 q^{92} + 27522 q^{93} + 28612 q^{94} + 16331 q^{95} + 53156 q^{96} + 15410 q^{97} + 34480 q^{98} + 24332 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.4.a \(\chi_{95}(1, \cdot)\) 95.4.a.a 1 1
95.4.a.b 1
95.4.a.c 1
95.4.a.d 1
95.4.a.e 3
95.4.a.f 5
95.4.a.g 6
95.4.b \(\chi_{95}(39, \cdot)\) 95.4.b.a 12 1
95.4.b.b 16
95.4.e \(\chi_{95}(11, \cdot)\) 95.4.e.a 2 2
95.4.e.b 18
95.4.e.c 20
95.4.g \(\chi_{95}(18, \cdot)\) 95.4.g.a 4 2
95.4.g.b 52
95.4.i \(\chi_{95}(49, \cdot)\) 95.4.i.a 56 2
95.4.k \(\chi_{95}(6, \cdot)\) 95.4.k.a 60 6
95.4.k.b 60
95.4.l \(\chi_{95}(8, \cdot)\) 95.4.l.a 112 4
95.4.p \(\chi_{95}(4, \cdot)\) 95.4.p.a 168 6
95.4.r \(\chi_{95}(2, \cdot)\) 95.4.r.a 336 12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)