Properties

Label 23.1.b
Level 23
Weight 1
Character orbit b
Rep. character \(\chi_{23}(22,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 23.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 23 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(23, [\chi])\).

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

\(q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut +\mathstrut q^{23} \) \(\mathstrut -\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut +\mathstrut q^{27} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut -\mathstrut q^{31} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut -\mathstrut q^{47} \) \(\mathstrut +\mathstrut q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut +\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut q^{62} \) \(\mathstrut +\mathstrut q^{64} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut q^{78} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut +\mathstrut q^{87} \) \(\mathstrut +\mathstrut q^{93} \) \(\mathstrut +\mathstrut q^{94} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(23, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.1.b.a \(1\) \(0.011\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-23}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{6}+q^{8}-q^{13}-q^{16}+\cdots\)