Properties

Label 36.6
Level 36
Weight 6
Dimension 78
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 432
Trace bound 3

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(432\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(36))\).

Total New Old
Modular forms 200 86 114
Cusp forms 160 78 82
Eisenstein series 40 8 32

Trace form

\( 78 q - 3 q^{2} + 12 q^{3} - 21 q^{4} - 81 q^{5} - 27 q^{6} + 177 q^{7} + 30 q^{9} + 600 q^{10} - 363 q^{11} - 486 q^{12} + 369 q^{13} - 1518 q^{14} + 117 q^{15} - 2169 q^{16} + 1686 q^{17} + 1992 q^{18}+ \cdots - 697239 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.6.a \(\chi_{36}(1, \cdot)\) 36.6.a.a 1 1
36.6.a.b 1
36.6.b \(\chi_{36}(35, \cdot)\) 36.6.b.a 2 1
36.6.b.b 8
36.6.e \(\chi_{36}(13, \cdot)\) 36.6.e.a 10 2
36.6.h \(\chi_{36}(11, \cdot)\) 36.6.h.a 56 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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