Properties

Label 287.2.u
Level 287
Weight 2
Character orbit u
Rep. character \(\chi_{287}(8,\cdot)\)
Character field \(\Q(\zeta_{20})\)
Dimension 160
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.u (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q(\zeta_{20})\)
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 240 160 80
Cusp forms 208 160 48
Eisenstein series 32 0 32

Trace form

\( 160q - 4q^{3} + 36q^{4} - 28q^{6} + O(q^{10}) \) \( 160q - 4q^{3} + 36q^{4} - 28q^{6} - 48q^{10} + 8q^{11} - 16q^{12} - 16q^{13} - 32q^{15} - 28q^{16} - 20q^{17} + 12q^{18} - 40q^{19} - 4q^{22} - 36q^{23} - 108q^{24} + 40q^{25} + 20q^{26} + 20q^{27} + 12q^{29} - 4q^{30} + 20q^{31} - 32q^{34} - 4q^{35} + 140q^{36} - 44q^{38} + 80q^{39} - 64q^{40} + 4q^{41} - 72q^{42} - 8q^{44} + 8q^{45} + 40q^{46} - 56q^{47} + 120q^{48} + 24q^{51} + 16q^{52} + 12q^{53} - 52q^{54} - 72q^{55} + 48q^{57} + 36q^{58} - 48q^{59} - 52q^{60} + 8q^{63} - 96q^{64} - 96q^{65} + 24q^{66} + 20q^{67} - 80q^{68} - 68q^{69} + 8q^{70} + 60q^{71} + 100q^{72} - 40q^{74} - 120q^{75} + 4q^{76} - 12q^{78} + 12q^{79} + 200q^{80} - 56q^{81} - 68q^{82} - 40q^{83} + 132q^{85} + 80q^{86} - 16q^{88} + 8q^{89} + 140q^{92} + 64q^{93} + 128q^{94} - 68q^{96} + 4q^{98} + 96q^{99} + O(q^{100}) \)

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.u.a \(160\) \(2.292\) None \(0\) \(-4\) \(0\) \(0\)

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

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