Properties

Label 287.2.l
Level 287
Weight 2
Character orbit l
Rep. character \(\chi_{287}(27,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 104
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.l (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{8})\)
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 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104q - 8q^{2} - 4q^{7} + 8q^{8} + 8q^{9} + O(q^{10}) \) \( 104q - 8q^{2} - 4q^{7} + 8q^{8} + 8q^{9} - 8q^{11} - 8q^{14} - 32q^{15} - 96q^{16} - 16q^{18} - 24q^{21} + 24q^{22} + 12q^{28} - 16q^{29} + 48q^{30} - 72q^{32} - 44q^{35} + 56q^{36} + 32q^{37} - 8q^{39} - 8q^{42} - 32q^{43} + 72q^{44} - 88q^{46} - 12q^{49} + 80q^{50} + 32q^{51} - 8q^{53} + 104q^{56} - 32q^{57} - 96q^{58} + 112q^{60} - 132q^{63} + 80q^{65} + 56q^{67} + 148q^{70} - 104q^{71} + 32q^{74} - 16q^{77} - 168q^{78} - 124q^{84} + 8q^{85} - 64q^{88} + 8q^{91} + 104q^{92} - 64q^{93} - 8q^{95} - 8q^{98} + 8q^{99} + O(q^{100}) \)

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.l.a \(104\) \(2.292\) None \(-8\) \(0\) \(0\) \(-4\)