Properties

Label 287.2.bb
Level 287
Weight 2
Character orbit bb
Rep. character \(\chi_{287}(6,\cdot)\)
Character field \(\Q(\zeta_{40})\)
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.bb (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{40})\)
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

\( 416q - 32q^{2} - 40q^{4} - 16q^{7} - 48q^{8} - 48q^{9} + O(q^{10}) \) \( 416q - 32q^{2} - 40q^{4} - 16q^{7} - 48q^{8} - 48q^{9} - 32q^{11} - 12q^{14} - 8q^{15} + 56q^{16} - 24q^{18} + 4q^{21} - 64q^{22} - 40q^{23} - 40q^{25} - 32q^{28} - 24q^{29} - 8q^{30} + 32q^{32} - 16q^{35} - 96q^{36} + 48q^{37} - 32q^{39} - 192q^{42} - 8q^{43} + 128q^{44} + 48q^{46} - 48q^{49} - 120q^{50} + 48q^{51} - 32q^{53} - 124q^{56} - 8q^{57} + 56q^{58} - 152q^{60} + 112q^{63} - 40q^{64} - 120q^{65} - 96q^{67} + 32q^{70} + 64q^{71} - 40q^{72} - 72q^{74} + 76q^{77} + 128q^{78} - 40q^{79} + 304q^{84} - 48q^{85} - 40q^{86} + 24q^{88} + 132q^{91} - 144q^{92} + 24q^{93} - 32q^{95} + 88q^{98} - 48q^{99} + O(q^{100}) \)

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.bb.a \(416\) \(2.292\) None \(-32\) \(0\) \(0\) \(-16\)