Properties

Label 69.2
Level 69
Weight 2
Dimension 109
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 704
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(69))\).

Total New Old
Modular forms 220 153 67
Cusp forms 133 109 24
Eisenstein series 87 44 43

Trace form

\( 109 q - 3 q^{2} - 12 q^{3} - 29 q^{4} - 6 q^{5} - 14 q^{6} - 30 q^{7} - 15 q^{8} - 12 q^{9} - 40 q^{10} - 12 q^{11} - 18 q^{12} - 36 q^{13} - 24 q^{14} - 6 q^{15} - 9 q^{16} + 4 q^{17} + 30 q^{18} - 20 q^{19}+ \cdots + 131 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)

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
69.2.a \(\chi_{69}(1, \cdot)\) 69.2.a.a 1 1
69.2.a.b 2
69.2.c \(\chi_{69}(68, \cdot)\) 69.2.c.a 6 1
69.2.e \(\chi_{69}(4, \cdot)\) 69.2.e.a 10 10
69.2.e.b 10
69.2.e.c 20
69.2.g \(\chi_{69}(5, \cdot)\) 69.2.g.a 60 10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)