Properties

Label 32.6
Level 32
Weight 6
Dimension 85
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(32))\).

Total New Old
Modular forms 176 95 81
Cusp forms 144 85 59
Eisenstein series 32 10 22

Trace form

\( 85 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 34 q^{5} - 4 q^{6} - 100 q^{7} - 4 q^{8} + 281 q^{9} - 204 q^{10} - 4 q^{11} - 1588 q^{12} + 106 q^{13} + 2476 q^{14} + 416 q^{15} + 4176 q^{16} + 1810 q^{17} - 1624 q^{18}+ \cdots + 338544 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)

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
32.6.a \(\chi_{32}(1, \cdot)\) 32.6.a.a 1 1
32.6.a.b 1
32.6.a.c 1
32.6.a.d 2
32.6.b \(\chi_{32}(17, \cdot)\) 32.6.b.a 4 1
32.6.e \(\chi_{32}(9, \cdot)\) None 0 2
32.6.g \(\chi_{32}(5, \cdot)\) 32.6.g.a 76 4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

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