Properties

Label 23.5.b
Level $23$
Weight $5$
Character orbit 23.b
Rep. character $\chi_{23}(22,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $10$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 23.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(23, [\chi])\).

Total New Old
Modular forms 9 9 0
Cusp forms 7 7 0
Eisenstein series 2 2 0

Trace form

\( 7 q - 8 q^{2} - 12 q^{3} + 24 q^{4} + 99 q^{6} - 157 q^{8} + 171 q^{9} + O(q^{10}) \) \( 7 q - 8 q^{2} - 12 q^{3} + 24 q^{4} + 99 q^{6} - 157 q^{8} + 171 q^{9} - 501 q^{12} - 4 q^{13} + 656 q^{16} - 861 q^{18} + 623 q^{23} + 3120 q^{24} - 737 q^{25} - 2485 q^{26} - 150 q^{27} + 1060 q^{29} + 908 q^{31} - 2160 q^{32} + 792 q^{35} + 2019 q^{36} - 5646 q^{39} + 772 q^{41} - 304 q^{46} + 12604 q^{47} - 19341 q^{48} - 7169 q^{49} - 680 q^{50} + 19467 q^{52} + 17955 q^{54} - 792 q^{55} + 475 q^{58} - 21074 q^{59} - 3949 q^{62} + 4291 q^{64} + 9588 q^{69} + 23184 q^{70} - 20588 q^{71} - 49677 q^{72} + 7916 q^{73} + 25548 q^{75} + 23976 q^{77} + 13731 q^{78} + 8343 q^{81} - 49637 q^{82} - 27144 q^{85} - 22230 q^{87} + 40104 q^{92} + 73770 q^{93} - 75389 q^{94} - 49536 q^{95} + 65139 q^{96} + 48760 q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.5.b.a 23.b 23.b $3$ $2.378$ 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-2\beta _{2})q^{2}+(6\beta _{1}-\beta _{2})q^{3}+(2^{4}+\cdots)q^{4}+\cdots\)
23.5.b.b 23.b 23.b $4$ $2.378$ \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(-8\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2-\beta _{3})q^{2}+(-3+3\beta _{3})q^{3}+(-6+\cdots)q^{4}+\cdots\)