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Properties

Label 1.82
Level 1
Weight 82
Dimension 6
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 82 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{82}(\Gamma_1(1))\).

Total New Old
Modular forms 7 7 0
Cusp forms 6 6 0
Eisenstein series 1 1 0

Trace form

\( 6 q - 460872026640 q^{2} - 15\!\cdots\!60 q^{3} + 44\!\cdots\!52 q^{4} - 18\!\cdots\!00 q^{5} + 79\!\cdots\!32 q^{6} - 31\!\cdots\!00 q^{7} - 54\!\cdots\!20 q^{8} + 11\!\cdots\!98 q^{9} - 66\!\cdots\!00 q^{10}+ \cdots - 63\!\cdots\!24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{82}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.82.a \(\chi_{1}(1, \cdot)\) 1.82.a.a 6 1