Properties

Label 59.1.b
Level 59
Weight 1
Character orbit b
Rep. character \(\chi_{59}(58,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 59.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 59 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(59, [\chi])\).

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

\(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut +\mathstrut q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut q^{53} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut +\mathstrut q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut 2q^{71} \) \(\mathstrut -\mathstrut q^{76} \) \(\mathstrut -\mathstrut q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut q^{84} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut q^{87} \) \(\mathstrut +\mathstrut q^{95} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(59, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
59.1.b.a \(1\) \(0.029\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-59}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q-q^{3}+q^{4}-q^{5}-q^{7}-q^{12}+q^{15}+\cdots\)