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Properties

Label 23.11.b
Level $23$
Weight $11$
Character orbit 23.b
Rep. character $\chi_{23}(22,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $2$
Sturm bound $22$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 11 \)
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: \(22\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(23, [\chi])\).

Total New Old
Modular forms 21 21 0
Cusp forms 19 19 0
Eisenstein series 2 2 0

Trace form

\( 19 q - 24 q^{2} + 60 q^{3} + 11688 q^{4} - 3357 q^{6} + 50571 q^{8} + 394839 q^{9} + O(q^{10}) \) \( 19 q - 24 q^{2} + 60 q^{3} + 11688 q^{4} - 3357 q^{6} + 50571 q^{8} + 394839 q^{9} + 311403 q^{12} - 615892 q^{13} + 2174480 q^{16} - 9424581 q^{18} + 2007675 q^{23} - 10437168 q^{24} - 32141045 q^{25} + 23555955 q^{26} + 27570522 q^{27} - 53419524 q^{29} + 142620860 q^{31} - 6579840 q^{32} - 28574160 q^{35} + 223540851 q^{36} - 165257598 q^{39} - 321041172 q^{41} - 819271744 q^{46} - 281525796 q^{47} + 450048555 q^{48} - 1306459757 q^{49} + 2674591320 q^{50} - 927498477 q^{52} + 597486267 q^{54} + 644578320 q^{55} + 3726333691 q^{58} + 886022382 q^{59} - 3283024077 q^{62} - 2375314061 q^{64} - 5154715140 q^{69} - 2550700320 q^{70} - 1890632532 q^{71} - 4269616413 q^{72} + 2852839868 q^{73} - 14004436980 q^{75} + 9446590224 q^{77} + 22788326643 q^{78} + 12152804139 q^{81} - 23541186101 q^{82} + 28868395440 q^{85} + 26987474322 q^{87} - 12603181368 q^{92} - 22156827222 q^{93} - 52082285717 q^{94} + 8158033920 q^{95} + 23957659131 q^{96} - 45996426408 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.11.b.a 23.b 23.b $3$ $14.613$ 3.3.621.1 \(\Q(\sqrt{-23}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-23\beta _{1}-2\beta _{2})q^{2}+(-66\beta _{1}+119\beta _{2})q^{3}+\cdots\)
23.11.b.b 23.b 23.b $16$ $14.613$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-24\) \(60\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+\beta _{2})q^{2}+(4-\beta _{2}-\beta _{3})q^{3}+\cdots\)