Properties

Label 3.8
Level 3
Weight 8
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(3))\).

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

Trace form

\( q + 6 q^{2} - 27 q^{3} - 92 q^{4} + 390 q^{5} - 162 q^{6} - 64 q^{7} - 1320 q^{8} + 729 q^{9} + 2340 q^{10} - 948 q^{11} + 2484 q^{12} - 5098 q^{13} - 384 q^{14} - 10530 q^{15} + 3856 q^{16} + 28386 q^{17}+ \cdots - 691092 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)

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
3.8.a \(\chi_{3}(1, \cdot)\) 3.8.a.a 1 1