Properties

Label 23.2.c
Level 23
Weight 2
Character orbit c
Rep. character \(\chi_{23}(2,\cdot)\)
Character field \(\Q(\zeta_{11})\)
Dimension 10
Newforms 1
Sturm bound 4
Trace bound 0

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 2 \)
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: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(23, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 10 10 0
Eisenstein series 20 20 0

Trace form

\(10q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(10q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 3q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut +\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut -\mathstrut 3q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 9q^{20} \) \(\mathstrut -\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 38q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut +\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 7q^{28} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 7q^{30} \) \(\mathstrut +\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 16q^{33} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut +\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 19q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut -\mathstrut 25q^{42} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut -\mathstrut 34q^{44} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut -\mathstrut 29q^{46} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 18q^{48} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut +\mathstrut 7q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut +\mathstrut 29q^{53} \) \(\mathstrut -\mathstrut 6q^{54} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut 2q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 21q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 3q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 34q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 2q^{66} \) \(\mathstrut +\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 30q^{68} \) \(\mathstrut +\mathstrut 26q^{69} \) \(\mathstrut +\mathstrut 38q^{70} \) \(\mathstrut -\mathstrut 14q^{71} \) \(\mathstrut +\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 10q^{74} \) \(\mathstrut -\mathstrut 28q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut -\mathstrut 52q^{80} \) \(\mathstrut -\mathstrut 44q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 17q^{84} \) \(\mathstrut -\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 27q^{88} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 20q^{90} \) \(\mathstrut -\mathstrut 4q^{91} \) \(\mathstrut +\mathstrut 52q^{92} \) \(\mathstrut +\mathstrut 4q^{93} \) \(\mathstrut +\mathstrut 17q^{94} \) \(\mathstrut +\mathstrut 6q^{95} \) \(\mathstrut -\mathstrut 51q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 17q^{98} \) \(\mathstrut -\mathstrut 30q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(23, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
23.2.c.a \(10\) \(0.184\) \(\Q(\zeta_{22})\) None \(-7\) \(-7\) \(-3\) \(-5\) \(q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots\)