Properties

Label 23.3.b
Level 23
Weight 3
Character orbit b
Rep. character \(\chi_{23}(22,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 23.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 23 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(23, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\(3q \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 33q^{6} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut -\mathstrut 33q^{6} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 39q^{18} \) \(\mathstrut -\mathstrut 69q^{23} \) \(\mathstrut -\mathstrut 132q^{24} \) \(\mathstrut +\mathstrut 75q^{25} \) \(\mathstrut +\mathstrut 87q^{26} \) \(\mathstrut -\mathstrut 114q^{27} \) \(\mathstrut -\mathstrut 84q^{32} \) \(\mathstrut +\mathstrut 255q^{36} \) \(\mathstrut -\mathstrut 42q^{39} \) \(\mathstrut +\mathstrut 231q^{48} \) \(\mathstrut +\mathstrut 147q^{49} \) \(\mathstrut -\mathstrut 309q^{52} \) \(\mathstrut -\mathstrut 297q^{54} \) \(\mathstrut -\mathstrut 273q^{58} \) \(\mathstrut +\mathstrut 78q^{59} \) \(\mathstrut +\mathstrut 303q^{62} \) \(\mathstrut -\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 33q^{72} \) \(\mathstrut +\mathstrut 399q^{78} \) \(\mathstrut +\mathstrut 243q^{81} \) \(\mathstrut -\mathstrut 129q^{82} \) \(\mathstrut +\mathstrut 246q^{87} \) \(\mathstrut -\mathstrut 276q^{92} \) \(\mathstrut -\mathstrut 546q^{93} \) \(\mathstrut -\mathstrut 57q^{94} \) \(\mathstrut -\mathstrut 21q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(23, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.3.b.a \(3\) \(0.627\) 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)