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Properties

Label 66.3
Level 66
Weight 3
Dimension 60
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 720
Trace bound 1

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Defining parameters

Level: \( N \) = \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(66))\).

Total New Old
Modular forms 280 60 220
Cusp forms 200 60 140
Eisenstein series 80 0 80

Trace form

\( 60 q + 20 q^{6} + 60 q^{7} + 20 q^{9} - 20 q^{11} - 20 q^{12} - 60 q^{13} - 80 q^{14} - 40 q^{15} - 60 q^{17} - 40 q^{18} + 60 q^{19} - 40 q^{23} - 40 q^{24} - 160 q^{25} - 150 q^{27} - 160 q^{29} - 60 q^{30}+ \cdots + 580 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(66))\)

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
66.3.c \(\chi_{66}(23, \cdot)\) 66.3.c.a 8 1
66.3.d \(\chi_{66}(43, \cdot)\) 66.3.d.a 4 1
66.3.f \(\chi_{66}(7, \cdot)\) 66.3.f.a 16 4
66.3.g \(\chi_{66}(5, \cdot)\) 66.3.g.a 32 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(66))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(66)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)