Properties

Label 27.5
Level 27
Weight 5
Dimension 77
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 270
Trace bound 1

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(270\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(27))\).

Total New Old
Modular forms 123 93 30
Cusp forms 93 77 16
Eisenstein series 30 16 14

Trace form

\( 77 q - 3 q^{2} - 6 q^{3} - 37 q^{4} + 15 q^{5} + 90 q^{6} + 73 q^{7} - 9 q^{8} - 108 q^{9} - 453 q^{10} - 975 q^{11} - 339 q^{12} + 445 q^{13} + 2283 q^{14} + 1017 q^{15} + 1187 q^{16} - 9 q^{17} + 603 q^{18}+ \cdots - 162405 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(27))\)

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
27.5.b \(\chi_{27}(26, \cdot)\) 27.5.b.a 1 1
27.5.b.b 2
27.5.b.c 2
27.5.d \(\chi_{27}(8, \cdot)\) 27.5.d.a 6 2
27.5.f \(\chi_{27}(2, \cdot)\) 27.5.f.a 66 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(27))\) into lower level spaces

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