Properties

Label 288.2.bf
Level 288
Weight 2
Character orbit bf
Rep. character \(\chi_{288}(11,\cdot)\)
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.bf (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

\( 368q - 12q^{2} - 8q^{3} - 4q^{4} - 12q^{5} - 8q^{6} - 4q^{7} - 8q^{9} + O(q^{10}) \) \( 368q - 12q^{2} - 8q^{3} - 4q^{4} - 12q^{5} - 8q^{6} - 4q^{7} - 8q^{9} - 16q^{10} - 12q^{11} - 8q^{12} - 4q^{13} - 12q^{14} - 16q^{15} - 4q^{16} - 8q^{18} - 16q^{19} - 12q^{20} - 8q^{21} - 4q^{22} - 12q^{23} + 32q^{24} - 4q^{25} + 16q^{27} - 16q^{28} - 12q^{29} - 56q^{30} - 12q^{32} - 16q^{33} - 12q^{34} - 60q^{36} - 16q^{37} - 12q^{38} + 16q^{39} - 4q^{40} - 12q^{41} - 8q^{42} - 4q^{43} - 8q^{45} - 16q^{46} - 24q^{47} - 60q^{48} - 168q^{50} - 32q^{51} - 4q^{52} - 52q^{54} - 16q^{55} - 12q^{56} - 8q^{57} + 32q^{58} - 12q^{59} - 20q^{60} - 4q^{61} - 16q^{64} - 24q^{65} - 80q^{66} - 4q^{67} - 60q^{68} - 8q^{69} - 4q^{70} + 52q^{72} - 16q^{73} - 12q^{74} - 28q^{75} - 28q^{76} - 12q^{77} + 80q^{78} - 8q^{79} - 16q^{82} - 132q^{83} - 104q^{84} - 24q^{85} - 12q^{86} - 64q^{87} - 4q^{88} + 124q^{90} - 16q^{91} + 216q^{92} - 20q^{93} - 20q^{94} + 92q^{96} - 8q^{97} - 72q^{99} + O(q^{100}) \)

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.bf.a \(368\) \(2.300\) None \(-12\) \(-8\) \(-12\) \(-4\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database