Properties

Label 27.6
Level 27
Weight 6
Dimension 99
Nonzero newspaces 3
Newform subspaces 6
Sturm bound 324
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 6 \)
Sturm bound: \(324\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(27))\).

Total New Old
Modular forms 150 115 35
Cusp forms 120 99 21
Eisenstein series 30 16 14

Trace form

\( 99 q - 9 q^{2} - 6 q^{3} + 63 q^{4} - 171 q^{5} - 126 q^{6} + 129 q^{7} + 1323 q^{8} + 324 q^{9} + 39 q^{10} - 333 q^{11} - 2769 q^{12} - 2841 q^{13} - 3033 q^{14} + 1989 q^{15} + 6051 q^{16} + 7821 q^{17}+ \cdots - 28323 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.6.a \(\chi_{27}(1, \cdot)\) 27.6.a.a 1 1
27.6.a.b 2
27.6.a.c 2
27.6.a.d 2
27.6.c \(\chi_{27}(10, \cdot)\) 27.6.c.a 8 2
27.6.e \(\chi_{27}(4, \cdot)\) 27.6.e.a 84 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(27)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)