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Properties

Label 23.7.d
Level $23$
Weight $7$
Character orbit 23.d
Rep. character $\chi_{23}(5,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $110$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 23.d (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(23, [\chi])\).

Total New Old
Modular forms 130 130 0
Cusp forms 110 110 0
Eisenstein series 20 20 0

Trace form

\( 110 q - 19 q^{2} - 41 q^{3} - 371 q^{4} - 11 q^{5} + 274 q^{6} - 11 q^{7} - 486 q^{8} - 644 q^{9} + O(q^{10}) \) \( 110 q - 19 q^{2} - 41 q^{3} - 371 q^{4} - 11 q^{5} + 274 q^{6} - 11 q^{7} - 486 q^{8} - 644 q^{9} - 11 q^{10} - 11 q^{11} - 374 q^{12} + 1095 q^{13} - 11 q^{14} + 10461 q^{15} - 36315 q^{16} - 11451 q^{17} + 14826 q^{18} + 15829 q^{19} + 78837 q^{20} + 40909 q^{21} - 14726 q^{23} - 171142 q^{24} - 51382 q^{25} - 24782 q^{26} - 72575 q^{27} + 101365 q^{28} + 144631 q^{29} + 311157 q^{30} + 87879 q^{31} - 219979 q^{32} - 234267 q^{33} + 400015 q^{34} - 215631 q^{35} - 459599 q^{36} - 446699 q^{37} - 275286 q^{38} - 123719 q^{39} + 626989 q^{40} + 20935 q^{41} + 1274119 q^{42} + 428989 q^{43} + 434434 q^{44} - 225219 q^{46} - 390212 q^{47} - 969358 q^{48} - 1114438 q^{49} - 1429656 q^{50} - 463331 q^{51} + 642832 q^{52} + 183909 q^{53} + 3498882 q^{54} + 708325 q^{55} + 175560 q^{56} + 78661 q^{57} - 1797805 q^{58} - 1172117 q^{59} - 2858581 q^{60} + 495253 q^{61} + 733266 q^{62} + 1713789 q^{63} + 1623458 q^{64} + 2406085 q^{65} + 2124936 q^{66} + 290389 q^{67} + 351879 q^{69} - 1394518 q^{70} - 1740145 q^{71} - 6508097 q^{72} - 511545 q^{73} - 1038180 q^{74} + 2544559 q^{75} - 1754258 q^{76} - 1625763 q^{77} - 6763872 q^{78} - 833723 q^{79} + 2796838 q^{80} - 346498 q^{81} + 169124 q^{82} + 2924229 q^{83} + 6932651 q^{84} + 3477625 q^{85} + 1596771 q^{86} + 9115465 q^{87} + 5363325 q^{88} + 2950849 q^{89} + 5004362 q^{90} + 52906 q^{92} - 4985338 q^{93} - 11378163 q^{94} - 5330019 q^{95} - 8886491 q^{96} - 6375215 q^{97} - 7997483 q^{98} - 16096091 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(23, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
23.7.d.a 23.d 23.d $110$ $5.291$ None \(-19\) \(-41\) \(-11\) \(-11\) $\mathrm{SU}(2)[C_{22}]$