Properties

Label 287.2.f
Level 287
Weight 2
Character orbit f
Rep. character \(\chi_{287}(50,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 40
Newforms 1
Sturm bound 56
Trace bound 0

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(287, [\chi])\).

Total New Old
Modular forms 60 40 20
Cusp forms 52 40 12
Eisenstein series 8 0 8

Trace form

\( 40q + 4q^{3} - 36q^{4} + 8q^{6} + O(q^{10}) \) \( 40q + 4q^{3} - 36q^{4} + 8q^{6} - 32q^{10} - 8q^{11} + 16q^{12} + 16q^{13} - 8q^{15} + 28q^{16} + 20q^{17} - 12q^{18} - 20q^{19} + 4q^{22} + 16q^{23} - 12q^{24} - 40q^{25} - 20q^{26} - 20q^{27} - 12q^{29} + 4q^{30} + 32q^{34} + 4q^{35} - 16q^{38} + 64q^{40} + 16q^{41} + 32q^{42} + 8q^{44} + 72q^{45} - 24q^{47} - 40q^{48} - 64q^{51} - 96q^{52} + 8q^{53} + 52q^{54} - 8q^{55} - 88q^{57} - 36q^{58} + 48q^{59} + 52q^{60} - 8q^{63} - 84q^{64} - 44q^{65} + 56q^{66} + 40q^{67} - 60q^{68} + 28q^{69} - 8q^{70} + 20q^{71} + 80q^{72} - 20q^{75} - 4q^{76} + 12q^{78} - 12q^{79} + 16q^{81} - 52q^{82} + 40q^{83} + 8q^{85} + 80q^{86} + 96q^{88} - 8q^{89} - 20q^{92} - 64q^{93} + 52q^{94} + 68q^{96} - 60q^{97} - 4q^{98} - 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(287, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
287.2.f.a \(40\) \(2.292\) None \(0\) \(4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)