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Properties

Label 2.88
Level 2
Weight 88
Dimension 7
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 22
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 88 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{88}(\Gamma_1(2))\).

Total New Old
Modular forms 23 7 16
Cusp forms 21 7 14
Eisenstein series 2 0 2

Trace form

\( 7 q - 8796093022208 q^{2} + 80\!\cdots\!12 q^{3} + 54\!\cdots\!48 q^{4} - 29\!\cdots\!10 q^{5} - 63\!\cdots\!52 q^{6} + 56\!\cdots\!16 q^{7} - 68\!\cdots\!12 q^{8} + 87\!\cdots\!39 q^{9} + 45\!\cdots\!80 q^{10}+ \cdots + 89\!\cdots\!08 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{88}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.88.a \(\chi_{2}(1, \cdot)\) 2.88.a.a 3 1
2.88.a.b 4

Decomposition of \(S_{88}^{\mathrm{old}}(\Gamma_1(2))\) into lower level spaces

\( S_{88}^{\mathrm{old}}(\Gamma_1(2)) \cong \) \(S_{88}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)