Properties

Label 23.3.d
Level 23
Weight 3
Character orbit d
Rep. character \(\chi_{23}(5,\cdot)\)
Character field \(\Q(\zeta_{22})\)
Dimension 30
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 23.d (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 23 \)
Character field: \(\Q(\zeta_{22})\)
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 50 50 0
Cusp forms 30 30 0
Eisenstein series 20 20 0

Trace form

\(30q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut -\mathstrut 23q^{4} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 10q^{8} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 11q^{3} \) \(\mathstrut -\mathstrut 23q^{4} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 10q^{8} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 11q^{10} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut -\mathstrut 14q^{12} \) \(\mathstrut -\mathstrut 11q^{13} \) \(\mathstrut -\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 66q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 44q^{17} \) \(\mathstrut +\mathstrut 126q^{18} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut +\mathstrut 77q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut -\mathstrut 22q^{24} \) \(\mathstrut -\mathstrut 152q^{25} \) \(\mathstrut -\mathstrut 186q^{26} \) \(\mathstrut -\mathstrut 62q^{27} \) \(\mathstrut -\mathstrut 275q^{28} \) \(\mathstrut -\mathstrut 88q^{29} \) \(\mathstrut -\mathstrut 363q^{30} \) \(\mathstrut -\mathstrut 110q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 132q^{33} \) \(\mathstrut +\mathstrut 231q^{34} \) \(\mathstrut +\mathstrut 209q^{35} \) \(\mathstrut +\mathstrut 229q^{36} \) \(\mathstrut +\mathstrut 341q^{37} \) \(\mathstrut +\mathstrut 374q^{38} \) \(\mathstrut +\mathstrut 295q^{39} \) \(\mathstrut +\mathstrut 429q^{40} \) \(\mathstrut +\mathstrut 77q^{41} \) \(\mathstrut +\mathstrut 319q^{42} \) \(\mathstrut +\mathstrut 77q^{43} \) \(\mathstrut +\mathstrut 110q^{44} \) \(\mathstrut -\mathstrut 99q^{46} \) \(\mathstrut -\mathstrut 110q^{47} \) \(\mathstrut -\mathstrut 550q^{48} \) \(\mathstrut -\mathstrut 422q^{49} \) \(\mathstrut -\mathstrut 396q^{50} \) \(\mathstrut -\mathstrut 275q^{51} \) \(\mathstrut -\mathstrut 472q^{52} \) \(\mathstrut -\mathstrut 187q^{53} \) \(\mathstrut -\mathstrut 198q^{54} \) \(\mathstrut -\mathstrut 165q^{55} \) \(\mathstrut +\mathstrut 176q^{56} \) \(\mathstrut -\mathstrut 176q^{57} \) \(\mathstrut -\mathstrut 13q^{58} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 539q^{60} \) \(\mathstrut +\mathstrut 297q^{61} \) \(\mathstrut +\mathstrut 82q^{62} \) \(\mathstrut +\mathstrut 264q^{63} \) \(\mathstrut +\mathstrut 386q^{64} \) \(\mathstrut +\mathstrut 220q^{65} \) \(\mathstrut +\mathstrut 264q^{66} \) \(\mathstrut +\mathstrut 11q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 198q^{70} \) \(\mathstrut -\mathstrut 176q^{71} \) \(\mathstrut -\mathstrut 605q^{72} \) \(\mathstrut -\mathstrut 121q^{73} \) \(\mathstrut -\mathstrut 352q^{74} \) \(\mathstrut +\mathstrut 154q^{75} \) \(\mathstrut +\mathstrut 110q^{76} \) \(\mathstrut +\mathstrut 110q^{77} \) \(\mathstrut +\mathstrut 360q^{78} \) \(\mathstrut +\mathstrut 33q^{79} \) \(\mathstrut -\mathstrut 242q^{80} \) \(\mathstrut +\mathstrut 494q^{81} \) \(\mathstrut +\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 154q^{83} \) \(\mathstrut +\mathstrut 11q^{84} \) \(\mathstrut +\mathstrut 275q^{85} \) \(\mathstrut +\mathstrut 143q^{86} \) \(\mathstrut +\mathstrut 271q^{87} \) \(\mathstrut +\mathstrut 429q^{88} \) \(\mathstrut +\mathstrut 121q^{89} \) \(\mathstrut +\mathstrut 242q^{90} \) \(\mathstrut +\mathstrut 166q^{92} \) \(\mathstrut +\mathstrut 260q^{93} \) \(\mathstrut -\mathstrut 295q^{94} \) \(\mathstrut -\mathstrut 154q^{95} \) \(\mathstrut -\mathstrut 419q^{96} \) \(\mathstrut +\mathstrut 154q^{97} \) \(\mathstrut +\mathstrut 77q^{98} \) \(\mathstrut -\mathstrut 242q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.d.a \(30\) \(0.627\) None \(-11\) \(-11\) \(-11\) \(-11\)