Properties

Label 23.4.c
Level 23
Weight 4
Character orbit c
Rep. character \(\chi_{23}(2,\cdot)\)
Character field \(\Q(\zeta_{11})\)
Dimension 50
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 23.c (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(23, [\chi])\).

Total New Old
Modular forms 70 70 0
Cusp forms 50 50 0
Eisenstein series 20 20 0

Trace form

\(50q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut -\mathstrut 27q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut -\mathstrut 27q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut +\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut 47q^{10} \) \(\mathstrut -\mathstrut 53q^{11} \) \(\mathstrut +\mathstrut 36q^{12} \) \(\mathstrut -\mathstrut 65q^{13} \) \(\mathstrut +\mathstrut 117q^{14} \) \(\mathstrut -\mathstrut 425q^{15} \) \(\mathstrut -\mathstrut 499q^{16} \) \(\mathstrut -\mathstrut 117q^{17} \) \(\mathstrut +\mathstrut 24q^{18} \) \(\mathstrut +\mathstrut 73q^{19} \) \(\mathstrut +\mathstrut 529q^{20} \) \(\mathstrut +\mathstrut 429q^{21} \) \(\mathstrut +\mathstrut 310q^{22} \) \(\mathstrut +\mathstrut 542q^{23} \) \(\mathstrut +\mathstrut 1606q^{24} \) \(\mathstrut +\mathstrut 246q^{25} \) \(\mathstrut +\mathstrut 324q^{26} \) \(\mathstrut +\mathstrut 65q^{27} \) \(\mathstrut -\mathstrut 677q^{28} \) \(\mathstrut -\mathstrut 497q^{29} \) \(\mathstrut -\mathstrut 1041q^{30} \) \(\mathstrut -\mathstrut 471q^{31} \) \(\mathstrut -\mathstrut 915q^{32} \) \(\mathstrut -\mathstrut 391q^{33} \) \(\mathstrut -\mathstrut 2751q^{34} \) \(\mathstrut -\mathstrut 737q^{35} \) \(\mathstrut -\mathstrut 1865q^{36} \) \(\mathstrut -\mathstrut 1071q^{37} \) \(\mathstrut -\mathstrut 1504q^{38} \) \(\mathstrut +\mathstrut 127q^{39} \) \(\mathstrut +\mathstrut 1479q^{40} \) \(\mathstrut +\mathstrut 569q^{41} \) \(\mathstrut +\mathstrut 3059q^{42} \) \(\mathstrut +\mathstrut 1615q^{43} \) \(\mathstrut +\mathstrut 2518q^{44} \) \(\mathstrut +\mathstrut 2768q^{45} \) \(\mathstrut +\mathstrut 4041q^{46} \) \(\mathstrut +\mathstrut 2904q^{47} \) \(\mathstrut +\mathstrut 2702q^{48} \) \(\mathstrut +\mathstrut 1226q^{49} \) \(\mathstrut +\mathstrut 1322q^{50} \) \(\mathstrut +\mathstrut 589q^{51} \) \(\mathstrut -\mathstrut 2156q^{52} \) \(\mathstrut +\mathstrut 391q^{53} \) \(\mathstrut -\mathstrut 5862q^{54} \) \(\mathstrut -\mathstrut 3323q^{55} \) \(\mathstrut -\mathstrut 7028q^{56} \) \(\mathstrut -\mathstrut 7623q^{57} \) \(\mathstrut -\mathstrut 5639q^{58} \) \(\mathstrut -\mathstrut 2445q^{59} \) \(\mathstrut -\mathstrut 3157q^{60} \) \(\mathstrut -\mathstrut 1059q^{61} \) \(\mathstrut +\mathstrut 1468q^{62} \) \(\mathstrut +\mathstrut 3155q^{63} \) \(\mathstrut +\mathstrut 4570q^{64} \) \(\mathstrut +\mathstrut 2641q^{65} \) \(\mathstrut +\mathstrut 5206q^{66} \) \(\mathstrut +\mathstrut 27q^{67} \) \(\mathstrut +\mathstrut 8350q^{68} \) \(\mathstrut +\mathstrut 4005q^{69} \) \(\mathstrut +\mathstrut 9702q^{70} \) \(\mathstrut +\mathstrut 3465q^{71} \) \(\mathstrut +\mathstrut 5629q^{72} \) \(\mathstrut +\mathstrut 435q^{73} \) \(\mathstrut -\mathstrut 994q^{74} \) \(\mathstrut -\mathstrut 7819q^{75} \) \(\mathstrut -\mathstrut 3598q^{76} \) \(\mathstrut -\mathstrut 5931q^{77} \) \(\mathstrut -\mathstrut 8996q^{78} \) \(\mathstrut -\mathstrut 2559q^{79} \) \(\mathstrut -\mathstrut 14052q^{80} \) \(\mathstrut -\mathstrut 4788q^{81} \) \(\mathstrut -\mathstrut 3822q^{82} \) \(\mathstrut -\mathstrut 3967q^{83} \) \(\mathstrut -\mathstrut 8427q^{84} \) \(\mathstrut +\mathstrut 299q^{85} \) \(\mathstrut +\mathstrut 721q^{86} \) \(\mathstrut +\mathstrut 8363q^{87} \) \(\mathstrut +\mathstrut 5825q^{88} \) \(\mathstrut +\mathstrut 3717q^{89} \) \(\mathstrut +\mathstrut 16742q^{90} \) \(\mathstrut +\mathstrut 7238q^{91} \) \(\mathstrut +\mathstrut 9550q^{92} \) \(\mathstrut +\mathstrut 12750q^{93} \) \(\mathstrut +\mathstrut 6035q^{94} \) \(\mathstrut +\mathstrut 4551q^{95} \) \(\mathstrut +\mathstrut 2493q^{96} \) \(\mathstrut -\mathstrut 2419q^{97} \) \(\mathstrut -\mathstrut 5687q^{98} \) \(\mathstrut -\mathstrut 755q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(23, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.4.c.a \(50\) \(1.357\) None \(-11\) \(-13\) \(-19\) \(-19\)