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Properties

Label 39.2
Level 39
Weight 2
Dimension 29
Nonzero newspaces 6
Newform subspaces 9
Sturm bound 224
Trace bound 3

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Defining parameters

Level: \( N \) = \( 39 = 3 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 9 \)
Sturm bound: \(224\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(39))\).

Total New Old
Modular forms 80 53 27
Cusp forms 33 29 4
Eisenstein series 47 24 23

Trace form

\( 29 q - 3 q^{2} - 7 q^{3} - 19 q^{4} - 6 q^{5} - 9 q^{6} - 16 q^{7} + 3 q^{8} - 5 q^{9} + 13 q^{12} - q^{13} - 3 q^{16} + 15 q^{18} + 8 q^{19} + 24 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} - q^{25} + 21 q^{26}+ \cdots + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)

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
39.2.a \(\chi_{39}(1, \cdot)\) 39.2.a.a 1 1
39.2.a.b 2
39.2.b \(\chi_{39}(25, \cdot)\) 39.2.b.a 2 1
39.2.e \(\chi_{39}(16, \cdot)\) 39.2.e.a 2 2
39.2.e.b 4
39.2.f \(\chi_{39}(5, \cdot)\) 39.2.f.a 4 2
39.2.j \(\chi_{39}(4, \cdot)\) 39.2.j.a 2 2
39.2.k \(\chi_{39}(2, \cdot)\) 39.2.k.a 4 4
39.2.k.b 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(39))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(39)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)