Properties

Label 95.5
Level 95
Weight 5
Dimension 1262
Nonzero newspaces 9
Newform subspaces 13
Sturm bound 3600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 95 = 5 \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 13 \)
Sturm bound: \(3600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(95))\).

Total New Old
Modular forms 1512 1362 150
Cusp forms 1368 1262 106
Eisenstein series 144 100 44

Trace form

\( 1262 q - 14 q^{2} + 6 q^{3} - 18 q^{4} - 107 q^{5} - 102 q^{6} + 86 q^{7} + 102 q^{8} - 18 q^{9} - 7 q^{10} - 22 q^{11} - 2082 q^{12} - 454 q^{13} + 1710 q^{14} + 1947 q^{15} + 4634 q^{16} + 580 q^{17}+ \cdots + 128070 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.5.c \(\chi_{95}(56, \cdot)\) 95.5.c.a 28 1
95.5.d \(\chi_{95}(94, \cdot)\) 95.5.d.a 2 1
95.5.d.b 2
95.5.d.c 2
95.5.d.d 4
95.5.d.e 28
95.5.f \(\chi_{95}(58, \cdot)\) 95.5.f.a 72 2
95.5.h \(\chi_{95}(69, \cdot)\) 95.5.h.a 76 2
95.5.j \(\chi_{95}(31, \cdot)\) 95.5.j.a 56 2
95.5.m \(\chi_{95}(7, \cdot)\) 95.5.m.a 152 4
95.5.n \(\chi_{95}(21, \cdot)\) 95.5.n.a 156 6
95.5.o \(\chi_{95}(14, \cdot)\) 95.5.o.a 228 6
95.5.q \(\chi_{95}(17, \cdot)\) 95.5.q.a 456 12

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

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