Properties

Label 32.9
Level 32
Weight 9
Dimension 139
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 576
Trace bound 1

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Defining parameters

Level: \( N \) = \( 32 = 2^{5} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(576\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(32))\).

Total New Old
Modular forms 272 149 123
Cusp forms 240 139 101
Eisenstein series 32 10 22

Trace form

\( 139 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 332 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 2759 q^{9} + 34996 q^{10} - 19778 q^{11} - 45364 q^{12} + 79948 q^{13} + 145580 q^{14} - 8 q^{15} - 278384 q^{16} - 182114 q^{17}+ \cdots - 1075195778 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(32))\)

We only show spaces with odd 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
32.9.c \(\chi_{32}(31, \cdot)\) 32.9.c.a 4 1
32.9.c.b 4
32.9.d \(\chi_{32}(15, \cdot)\) 32.9.d.a 1 1
32.9.d.b 6
32.9.f \(\chi_{32}(7, \cdot)\) None 0 2
32.9.h \(\chi_{32}(3, \cdot)\) 32.9.h.a 124 4

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(32))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(32)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)