Properties

Label 36.4
Level 36
Weight 4
Dimension 45
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 288
Trace bound 3

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(36))\).

Total New Old
Modular forms 128 53 75
Cusp forms 88 45 43
Eisenstein series 40 8 32

Trace form

\( 45 q - 3 q^{2} - 3 q^{3} + 11 q^{4} + 18 q^{5} + 21 q^{6} + 2 q^{7} + 45 q^{9} - 152 q^{10} + 15 q^{11} - 6 q^{12} + 72 q^{13} - 78 q^{14} - 180 q^{15} + 263 q^{16} - 240 q^{17} - 120 q^{18} - 70 q^{19}+ \cdots - 1854 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.4.a \(\chi_{36}(1, \cdot)\) 36.4.a.a 1 1
36.4.b \(\chi_{36}(35, \cdot)\) 36.4.b.a 2 1
36.4.b.b 4
36.4.e \(\chi_{36}(13, \cdot)\) 36.4.e.a 6 2
36.4.h \(\chi_{36}(11, \cdot)\) 36.4.h.a 8 2
36.4.h.b 24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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