Properties

Label 96.2
Level 96
Weight 2
Dimension 98
Nonzero newspaces 6
Newform subspaces 7
Sturm bound 1024
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 7 \)
Sturm bound: \(1024\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(96))\).

Total New Old
Modular forms 320 118 202
Cusp forms 193 98 95
Eisenstein series 127 20 107

Trace form

\( 98 q - 2 q^{3} - 8 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 2 q^{9} - 24 q^{10} - 20 q^{12} - 20 q^{13} - 32 q^{14} - 12 q^{15} - 48 q^{16} - 16 q^{17} - 12 q^{18} - 12 q^{19} - 32 q^{20} - 20 q^{21} - 32 q^{22}+ \cdots + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)

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
96.2.a \(\chi_{96}(1, \cdot)\) 96.2.a.a 1 1
96.2.a.b 1
96.2.c \(\chi_{96}(95, \cdot)\) 96.2.c.a 4 1
96.2.d \(\chi_{96}(49, \cdot)\) 96.2.d.a 2 1
96.2.f \(\chi_{96}(47, \cdot)\) 96.2.f.a 2 1
96.2.j \(\chi_{96}(25, \cdot)\) None 0 2
96.2.k \(\chi_{96}(23, \cdot)\) None 0 2
96.2.n \(\chi_{96}(13, \cdot)\) 96.2.n.a 32 4
96.2.o \(\chi_{96}(11, \cdot)\) 96.2.o.a 56 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(96))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(96)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)