Properties

Label 287.2.bc
Level 287
Weight 2
Character orbit bc
Rep. character \(\chi_{287}(2,\cdot)\)
Character field \(\Q(\zeta_{60})\)
Dimension 416
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.bc (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{60})\)
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 480 480 0
Cusp forms 416 416 0
Eisenstein series 64 64 0

Trace form

\( 416q - 10q^{2} - 8q^{3} - 54q^{4} - 10q^{5} - 16q^{6} - 16q^{7} - 40q^{8} + O(q^{10}) \) \( 416q - 10q^{2} - 8q^{3} - 54q^{4} - 10q^{5} - 16q^{6} - 16q^{7} - 40q^{8} + 18q^{10} - 12q^{11} - 24q^{12} - 32q^{13} + 10q^{14} - 32q^{15} + 26q^{16} - 2q^{17} - 30q^{18} - 4q^{19} + 80q^{20} - 20q^{21} - 32q^{22} - 6q^{23} + 26q^{24} - 42q^{25} - 18q^{26} - 92q^{27} - 42q^{28} - 128q^{29} - 38q^{30} - 38q^{31} + 100q^{33} - 56q^{34} - 2q^{35} - 120q^{36} + 6q^{38} - 10q^{39} + 20q^{40} - 44q^{41} + 112q^{42} - 76q^{44} - 106q^{45} + 90q^{46} + 32q^{47} - 20q^{48} - 48q^{51} - 20q^{52} - 2q^{53} + 72q^{54} - 16q^{55} - 166q^{56} - 32q^{57} - 14q^{58} + 54q^{59} + 62q^{60} - 90q^{61} - 40q^{62} - 100q^{63} - 8q^{64} + 2q^{65} + 22q^{66} - 24q^{67} - 42q^{68} + 24q^{69} + 222q^{70} - 92q^{71} - 30q^{72} - 10q^{74} - 32q^{75} + 348q^{76} + 80q^{77} + 80q^{78} + 10q^{79} - 90q^{80} + 120q^{81} - 124q^{82} + 432q^{83} + 76q^{85} - 54q^{86} - 10q^{87} - 130q^{88} - 50q^{89} + 80q^{90} - 92q^{92} - 16q^{93} - 50q^{94} - 52q^{95} - 64q^{96} - 4q^{97} + 66q^{98} - 124q^{99} + O(q^{100}) \)

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.bc.a \(416\) \(2.292\) None \(-10\) \(-8\) \(-10\) \(-16\)