Properties

Label 81.5
Level 81
Weight 5
Dimension 740
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 2430
Trace bound 1

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Defining parameters

Level: \( N \) = \( 81 = 3^{4} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(2430\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(81))\).

Total New Old
Modular forms 1026 796 230
Cusp forms 918 740 178
Eisenstein series 108 56 52

Trace form

\( 740 q - 12 q^{2} - 18 q^{3} - 4 q^{4} - 21 q^{5} - 18 q^{6} - 59 q^{7} - 9 q^{8} - 18 q^{9} + 195 q^{10} + 474 q^{11} - 18 q^{12} - 245 q^{13} - 1155 q^{14} - 18 q^{15} - 760 q^{16} - 9 q^{17} - 2034 q^{18}+ \cdots + 4266 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.5.b \(\chi_{81}(80, \cdot)\) 81.5.b.a 6 1
81.5.b.b 8
81.5.d \(\chi_{81}(26, \cdot)\) 81.5.d.a 2 2
81.5.d.b 4
81.5.d.c 4
81.5.d.d 4
81.5.d.e 16
81.5.f \(\chi_{81}(8, \cdot)\) 81.5.f.a 66 6
81.5.h \(\chi_{81}(2, \cdot)\) 81.5.h.a 630 18

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(81)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)