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Properties

Label 1.88
Level 1
Weight 88
Dimension 7
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 88 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{88}(\Gamma_1(1))\).

Total New Old
Modular forms 8 8 0
Cusp forms 7 7 0
Eisenstein series 1 1 0

Trace form

\( 7 q + 18197022042936 q^{2} - 75\!\cdots\!48 q^{3} + 37\!\cdots\!36 q^{4} + 33\!\cdots\!50 q^{5} + 16\!\cdots\!44 q^{6} + 45\!\cdots\!56 q^{7} + 27\!\cdots\!40 q^{8} + 67\!\cdots\!39 q^{9} - 36\!\cdots\!00 q^{10}+ \cdots + 15\!\cdots\!08 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{88}^{\mathrm{new}}(\Gamma_1(1))\)

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
1.88.a \(\chi_{1}(1, \cdot)\) 1.88.a.a 7 1