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

\( 934 q - 10 q^{2} - 22 q^{3} - 34 q^{4} - 17 q^{5} - 38 q^{6} - 30 q^{7} - 18 q^{8} + 28 q^{9} - 67 q^{10} - 118 q^{11} + 526 q^{12} + 346 q^{13} + 102 q^{14} - 115 q^{15} - 790 q^{16} - 358 q^{17} - 1156 q^{18}+ \cdots + 24332 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

\( S_{4}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)