Properties

Label 5.12
Level 5
Weight 12
Dimension 7
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(5))\).

Total New Old
Modular forms 13 9 4
Cusp forms 9 7 2
Eisenstein series 4 2 2

Trace form

\( 7 q + 14 q^{2} - 1012 q^{3} + 6012 q^{4} - 3425 q^{5} + 31504 q^{6} + 40344 q^{7} - 346200 q^{8} + 454723 q^{9} + 260150 q^{10} - 1413316 q^{11} - 1220576 q^{12} + 3040218 q^{13} + 1818264 q^{14} + 1645700 q^{15}+ \cdots + 27251190476 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.12.a \(\chi_{5}(1, \cdot)\) 5.12.a.a 1 1
5.12.a.b 2
5.12.b \(\chi_{5}(4, \cdot)\) 5.12.b.a 4 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)