Properties

Label 39.1
Level 39
Weight 1
Dimension 1
Nonzero newspaces 1
Newforms 1
Sturm bound 112
Trace bound 0

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Defining parameters

Level: \( N \) = \( 39 = 3 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newforms: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(39))\).

Total New Old
Modular forms 25 11 14
Cusp forms 1 1 0
Eisenstein series 24 10 14

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut q^{12} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut q^{36} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut +\mathstrut q^{52} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut q^{75} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
39.1.c \(\chi_{39}(14, \cdot)\) None 0 1
39.1.d \(\chi_{39}(38, \cdot)\) 39.1.d.a 1 1
39.1.g \(\chi_{39}(31, \cdot)\) None 0 2
39.1.h \(\chi_{39}(17, \cdot)\) None 0 2
39.1.i \(\chi_{39}(29, \cdot)\) None 0 2
39.1.l \(\chi_{39}(7, \cdot)\) None 0 4