Properties

Label 3.12
Level 3
Weight 12
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(3))\).

Total New Old
Modular forms 5 1 4
Cusp forms 3 1 2
Eisenstein series 2 0 2

Trace form

\( q + 78 q^{2} - 243 q^{3} + 4036 q^{4} - 5370 q^{5} - 18954 q^{6} - 27760 q^{7} + 155064 q^{8} + 59049 q^{9} - 418860 q^{10} + 637836 q^{11} - 980748 q^{12} + 766214 q^{13} - 2165280 q^{14} + 1304910 q^{15}+ \cdots + 37663577964 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.12.a \(\chi_{3}(1, \cdot)\) 3.12.a.a 1 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

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