Properties

Label 24.4
Level 24
Weight 4
Dimension 17
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(24))\).

Total New Old
Modular forms 60 21 39
Cusp forms 36 17 19
Eisenstein series 24 4 20

Trace form

\( 17 q + 2 q^{2} + q^{3} + 20 q^{4} + 14 q^{5} - 14 q^{6} + 4 q^{7} - 76 q^{8} - 47 q^{9} + 36 q^{10} - 28 q^{11} - 56 q^{12} - 74 q^{13} - 100 q^{14} - 18 q^{15} - 96 q^{16} + 134 q^{17} + 166 q^{18} + 64 q^{19}+ \cdots + 3860 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.4.a \(\chi_{24}(1, \cdot)\) 24.4.a.a 1 1
24.4.c \(\chi_{24}(23, \cdot)\) None 0 1
24.4.d \(\chi_{24}(13, \cdot)\) 24.4.d.a 6 1
24.4.f \(\chi_{24}(11, \cdot)\) 24.4.f.a 2 1
24.4.f.b 8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)