Properties

Label 108.6
Level 108
Weight 6
Dimension 731
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 3888
Trace bound 1

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(3888\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(108))\).

Total New Old
Modular forms 1695 763 932
Cusp forms 1545 731 814
Eisenstein series 150 32 118

Trace form

\( 731 q - 3 q^{2} + 3 q^{4} - 72 q^{5} - 6 q^{6} - 2 q^{7} - 9 q^{8} + 318 q^{9} - 405 q^{10} - 1434 q^{11} + 1173 q^{12} + 568 q^{13} + 3027 q^{14} + 531 q^{15} - 2685 q^{16} - 5766 q^{17} - 5697 q^{18}+ \cdots + 13635 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)

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
108.6.a \(\chi_{108}(1, \cdot)\) 108.6.a.a 1 1
108.6.a.b 2
108.6.a.c 2
108.6.a.d 2
108.6.b \(\chi_{108}(107, \cdot)\) 108.6.b.a 4 1
108.6.b.b 16
108.6.b.c 20
108.6.e \(\chi_{108}(37, \cdot)\) 108.6.e.a 10 2
108.6.h \(\chi_{108}(35, \cdot)\) 108.6.h.a 56 2
108.6.i \(\chi_{108}(13, \cdot)\) 108.6.i.a 90 6
108.6.l \(\chi_{108}(11, \cdot)\) 108.6.l.a 528 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)