Properties

Label 123.2.n
Level 123
Weight 2
Character orbit n
Rep. character \(\chi_{123}(43,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 48
Newforms 1
Sturm bound 28
Trace bound 0

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Defining parameters

Level: \( N \) = \( 123 = 3 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 123.n (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Newforms: \( 1 \)
Sturm bound: \(28\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(123, [\chi])\).

Total New Old
Modular forms 128 48 80
Cusp forms 96 48 48
Eisenstein series 32 0 32

Trace form

\( 48q + 8q^{4} + O(q^{10}) \) \( 48q + 8q^{4} - 16q^{10} + 12q^{11} - 8q^{12} - 4q^{13} - 20q^{14} - 16q^{15} - 8q^{17} - 4q^{19} - 60q^{20} - 12q^{22} - 12q^{23} - 12q^{24} + 28q^{25} + 20q^{26} - 56q^{28} - 12q^{29} - 16q^{30} + 8q^{31} + 32q^{34} + 4q^{35} + 16q^{37} - 80q^{38} + 64q^{40} + 40q^{41} - 8q^{42} - 20q^{43} + 100q^{44} - 8q^{45} - 60q^{46} + 20q^{47} + 16q^{48} + 40q^{49} + 12q^{51} + 20q^{52} + 32q^{53} - 64q^{55} + 40q^{56} - 16q^{57} - 36q^{58} - 24q^{59} + 4q^{60} - 40q^{61} + 8q^{64} - 144q^{65} + 24q^{66} - 16q^{67} + 96q^{68} + 20q^{69} + 16q^{70} + 72q^{71} + 24q^{72} - 40q^{74} + 40q^{75} + 112q^{76} + 20q^{77} + 44q^{78} + 80q^{80} - 48q^{81} + 20q^{82} + 40q^{83} - 56q^{85} + 112q^{86} + 40q^{87} - 56q^{88} + 64q^{89} + 60q^{90} + 12q^{92} + 48q^{93} - 44q^{94} + 52q^{95} + 4q^{96} - 60q^{97} + 20q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(123, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
123.2.n.a \(48\) \(0.982\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(123, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(123, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)