Properties

Label 1.12
Level 1
Weight 12
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 1
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(1\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(1))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 0
Eisenstein series 1 1 0

Trace form

\( q - 24 q^{2} + 252 q^{3} - 1472 q^{4} + 4830 q^{5} - 6048 q^{6} - 16744 q^{7} + 84480 q^{8} - 113643 q^{9} - 115920 q^{10} + 534612 q^{11} - 370944 q^{12} - 577738 q^{13} + 401856 q^{14} + 1217160 q^{15}+ \cdots - 60754911516 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.12.a \(\chi_{1}(1, \cdot)\) 1.12.a.a 1 1