Properties

Label 32.4
Level 32
Weight 4
Dimension 49
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 256
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(256\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(32))\).

Total New Old
Modular forms 112 59 53
Cusp forms 80 49 31
Eisenstein series 32 10 22

Trace form

\( 49 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{7} - 4 q^{8} + 41 q^{9} + 116 q^{10} - 4 q^{11} - 52 q^{12} - 122 q^{13} - 212 q^{14} - 112 q^{15} - 304 q^{16} - 182 q^{17} - 184 q^{18} - 4 q^{19}+ \cdots - 5424 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.4.a \(\chi_{32}(1, \cdot)\) 32.4.a.a 1 1
32.4.a.b 1
32.4.a.c 1
32.4.b \(\chi_{32}(17, \cdot)\) 32.4.b.a 2 1
32.4.e \(\chi_{32}(9, \cdot)\) None 0 2
32.4.g \(\chi_{32}(5, \cdot)\) 32.4.g.a 44 4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)