Properties

Label 39.1.d
Level 39
Weight 1
Character orbit d
Rep. character \(\chi_{39}(38,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 39 = 3 \cdot 13 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 39.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 39 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(39, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

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 \(S_{1}^{\mathrm{new}}(39, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
39.1.d.a \(1\) \(0.019\) \(\Q\) \(D_{2}\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-39}) \) \(\Q(\sqrt{13}) \) \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots\)