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Properties

Label 23.3.b
Level $23$
Weight $3$
Character orbit 23.b
Rep. character $\chi_{23}(22,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.3.b.a 23.b 23.b $3$ $0.627$ 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-2\beta _{1}-\beta _{2})q^{3}+(4+\cdots)q^{4}+\cdots\)