Properties

Label 287.2.j
Level 287
Weight 2
Character orbit j
Rep. character \(\chi_{287}(81,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 52
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{6})\)
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 60 60 0
Cusp forms 52 52 0
Eisenstein series 8 8 0

Trace form

\( 52q - 2q^{2} - 26q^{4} - 6q^{5} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 52q - 2q^{2} - 26q^{4} - 6q^{5} - 12q^{8} + 16q^{9} + 16q^{10} - 26q^{16} + 12q^{18} + 16q^{20} - 48q^{21} - 32q^{25} + 6q^{31} + 20q^{32} - 20q^{33} - 4q^{36} - 24q^{37} + 14q^{39} + 44q^{40} + 24q^{41} - 2q^{42} - 32q^{43} + 26q^{45} + 12q^{46} + 16q^{49} - 12q^{51} + 8q^{57} + 2q^{59} + 14q^{61} - 20q^{62} - 20q^{64} - 4q^{66} - 42q^{72} - 16q^{73} - 22q^{74} - 32q^{77} + 88q^{78} - 52q^{80} - 46q^{81} - 42q^{82} - 112q^{83} + 72q^{84} + 16q^{86} - 18q^{87} + 224q^{90} + 86q^{91} - 32q^{92} - 48q^{98} + O(q^{100}) \)

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.j.a \(52\) \(2.292\) None \(-2\) \(0\) \(-6\) \(0\)