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Properties

Label 24.3
Level 24
Weight 3
Dimension 12
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(24))\).

Total New Old
Modular forms 44 16 28
Cusp forms 20 12 8
Eisenstein series 24 4 20

Trace form

\( 12 q + 2 q^{2} + 2 q^{3} - 12 q^{4} - 14 q^{6} - 16 q^{7} - 4 q^{8} - 4 q^{9} - 12 q^{10} - 32 q^{11} + 16 q^{12} + 20 q^{13} + 36 q^{14} + 12 q^{15} + 32 q^{16} - 8 q^{17} + 62 q^{18} + 36 q^{19} + 72 q^{20}+ \cdots - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.3.b \(\chi_{24}(19, \cdot)\) 24.3.b.a 4 1
24.3.e \(\chi_{24}(17, \cdot)\) 24.3.e.a 2 1
24.3.g \(\chi_{24}(7, \cdot)\) None 0 1
24.3.h \(\chi_{24}(5, \cdot)\) 24.3.h.a 1 1
24.3.h.b 1
24.3.h.c 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

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