Properties

Label 287.2.w
Level 287
Weight 2
Character orbit w
Rep. character \(\chi_{287}(3,\cdot)\)
Character field \(\Q(\zeta_{24})\)
Dimension 208
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.w (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{24})\)
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 240 240 0
Cusp forms 208 208 0
Eisenstein series 32 32 0

Trace form

\( 208q - 4q^{2} - 12q^{3} - 12q^{5} - 8q^{7} - 32q^{8} + 4q^{9} + O(q^{10}) \) \( 208q - 4q^{2} - 12q^{3} - 12q^{5} - 8q^{7} - 32q^{8} + 4q^{9} - 24q^{10} - 4q^{11} - 12q^{12} - 4q^{14} + 8q^{15} + 72q^{16} + 24q^{17} - 8q^{18} + 12q^{19} - 48q^{21} - 96q^{22} - 60q^{24} - 36q^{26} - 24q^{28} + 16q^{29} - 36q^{30} + 48q^{32} + 48q^{33} + 32q^{35} - 80q^{36} + 16q^{37} + 72q^{38} - 4q^{39} + 80q^{42} - 64q^{43} - 12q^{44} - 44q^{46} + 12q^{47} - 72q^{49} - 8q^{50} + 16q^{51} + 12q^{52} - 28q^{53} - 180q^{54} - 32q^{56} - 16q^{57} - 24q^{59} - 4q^{60} - 12q^{61} + 36q^{63} - 8q^{65} + 4q^{67} - 84q^{68} + 20q^{70} + 32q^{71} - 48q^{73} + 40q^{74} + 168q^{75} - 104q^{77} - 48q^{78} - 120q^{80} + 132q^{82} + 112q^{84} + 64q^{85} - 144q^{87} - 32q^{88} + 36q^{89} - 56q^{91} + 16q^{92} + 4q^{93} + 96q^{94} - 4q^{95} + 12q^{96} - 136q^{98} - 224q^{99} + O(q^{100}) \)

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.w.a \(208\) \(2.292\) None \(-4\) \(-12\) \(-12\) \(-8\)