Properties

Label 288.2.bc
Level 288
Weight 2
Character orbit bc
Rep. character \(\chi_{288}(13,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 368
Newform subspaces 1
Sturm bound 96
Trace bound 0

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Defining parameters

Level: \( N \) = \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 288.bc (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 288 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

Total New Old
Modular forms 400 400 0
Cusp forms 368 368 0
Eisenstein series 32 32 0

Trace form

\( 368q - 4q^{2} - 8q^{3} - 4q^{4} - 4q^{5} - 8q^{6} - 4q^{7} - 16q^{8} - 8q^{9} + O(q^{10}) \) \( 368q - 4q^{2} - 8q^{3} - 4q^{4} - 4q^{5} - 8q^{6} - 4q^{7} - 16q^{8} - 8q^{9} - 16q^{10} - 4q^{11} - 8q^{12} - 4q^{13} - 4q^{14} - 4q^{16} - 8q^{18} - 16q^{19} - 4q^{20} - 8q^{21} - 4q^{22} - 4q^{23} - 48q^{24} - 4q^{25} - 16q^{26} - 32q^{27} - 16q^{28} - 4q^{29} + 24q^{30} - 8q^{31} - 4q^{32} - 16q^{33} + 4q^{34} - 16q^{35} + 20q^{36} - 16q^{37} - 60q^{38} - 32q^{39} - 4q^{40} - 4q^{41} - 88q^{42} - 4q^{43} - 104q^{44} - 8q^{45} - 16q^{46} - 60q^{48} + 48q^{50} + 16q^{51} - 4q^{52} - 16q^{53} - 52q^{54} - 16q^{55} - 84q^{56} - 8q^{57} - 40q^{58} - 4q^{59} - 52q^{60} - 4q^{61} - 24q^{62} - 16q^{63} - 16q^{64} - 8q^{65} + 64q^{66} - 4q^{67} + 12q^{68} - 8q^{69} - 4q^{70} - 16q^{71} - 68q^{72} - 16q^{73} - 4q^{74} - 28q^{75} + 20q^{76} - 4q^{77} - 72q^{78} + 48q^{80} - 16q^{82} + 36q^{83} + 200q^{84} + 16q^{85} + 100q^{86} - 64q^{87} - 4q^{88} - 16q^{89} + 4q^{90} - 16q^{91} - 80q^{92} + 4q^{93} - 20q^{94} - 136q^{95} + 28q^{96} - 8q^{97} + 104q^{98} - 72q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.2.bc.a \(368\) \(2.300\) None \(-4\) \(-8\) \(-4\) \(-4\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database