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Properties

Label 4.22
Level 4
Weight 22
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 22
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(4))\).

Total New Old
Modular forms 12 2 10
Cusp forms 9 2 7
Eisenstein series 3 0 3

Trace form

\( 2 q + 65640 q^{3} + 13689324 q^{5} - 260508080 q^{7} + 12461535162 q^{9} + 145435963320 q^{11} + 1428900417340 q^{13} + 6819782714352 q^{15} + 1840620576420 q^{17} - 16780743928568 q^{19} - 192357511002048 q^{21}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.22.a \(\chi_{4}(1, \cdot)\) 4.22.a.a 2 1

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(4))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(4)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)