Properties

Label 81.3
Level 81
Weight 3
Dimension 356
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 1458
Trace bound 1

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Defining parameters

Level: \( N \) = \( 81 = 3^{4} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(1458\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(81))\).

Total New Old
Modular forms 540 412 128
Cusp forms 432 356 76
Eisenstein series 108 56 52

Trace form

\( 356 q - 12 q^{2} - 18 q^{3} - 16 q^{4} - 3 q^{5} - 18 q^{6} - 17 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 12 q^{11} - 18 q^{12} - 11 q^{13} - 3 q^{14} - 18 q^{15} - 52 q^{16} - 9 q^{17} - 90 q^{18} - 125 q^{19}+ \cdots - 1566 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(81))\)

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
81.3.b \(\chi_{81}(80, \cdot)\) 81.3.b.a 2 1
81.3.b.b 4
81.3.d \(\chi_{81}(26, \cdot)\) 81.3.d.a 2 2
81.3.d.b 4
81.3.d.c 8
81.3.f \(\chi_{81}(8, \cdot)\) 81.3.f.a 30 6
81.3.h \(\chi_{81}(2, \cdot)\) 81.3.h.a 306 18

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(81))\) into lower level spaces

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