Properties

Label 287.2.e
Level 287
Weight 2
Character orbit e
Rep. character \(\chi_{287}(165,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 52
Newforms 4
Sturm bound 56
Trace bound 2

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(287, [\chi])\).

Total New Old
Modular forms 60 52 8
Cusp forms 52 52 0
Eisenstein series 8 0 8

Trace form

\( 52q - 2q^{2} - 2q^{3} - 26q^{4} + 2q^{5} + 8q^{6} - 4q^{7} + 12q^{8} - 28q^{9} + O(q^{10}) \) \( 52q - 2q^{2} - 2q^{3} - 26q^{4} + 2q^{5} + 8q^{6} - 4q^{7} + 12q^{8} - 28q^{9} + 4q^{10} - 6q^{11} + 6q^{12} - 8q^{13} + 2q^{14} + 16q^{15} - 26q^{16} - 8q^{17} - 6q^{19} - 32q^{20} + 8q^{22} - 4q^{23} - 32q^{24} - 8q^{25} - 20q^{26} - 8q^{27} + 36q^{28} + 16q^{29} + 20q^{30} + 6q^{31} - 4q^{32} + 20q^{33} - 32q^{34} + 30q^{35} + 84q^{36} - 8q^{37} - 18q^{39} - 20q^{40} + 16q^{41} + 26q^{42} - 32q^{43} - 2q^{44} + 18q^{45} - 24q^{46} - 6q^{47} - 100q^{48} - 40q^{49} - 24q^{50} + 12q^{51} + 26q^{52} + 12q^{53} - 38q^{54} + 40q^{55} + 10q^{56} - 4q^{58} + 34q^{59} - 52q^{60} + 14q^{61} + 20q^{62} + 26q^{63} + 124q^{64} - 36q^{65} - 8q^{66} - 26q^{67} - 18q^{68} + 24q^{69} + 34q^{70} + 40q^{71} - 2q^{72} - 26q^{74} - 22q^{75} + 32q^{76} - 24q^{77} - 16q^{78} - 12q^{79} + 92q^{80} - 34q^{81} - 4q^{82} - 32q^{83} + 168q^{84} - 76q^{85} - 4q^{86} - 30q^{87} - 64q^{88} - 16q^{89} + 8q^{90} + 2q^{91} + 80q^{92} + 54q^{93} + 4q^{94} + 18q^{95} - 106q^{96} + 44q^{97} + 44q^{98} + 32q^{99} + O(q^{100}) \)

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.e.a \(4\) \(2.292\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(-2\) \(2\) \(-8\) \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
287.2.e.b \(4\) \(2.292\) \(\Q(\sqrt{-3}, \sqrt{13})\) None \(0\) \(-1\) \(1\) \(-2\) \(q-\beta _{1}q^{3}+(2+2\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
287.2.e.c \(10\) \(2.292\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(2\) \(-2\) \(8\) \(q-\beta _{7}q^{2}+\beta _{8}q^{3}+(\beta _{1}-\beta _{2}-\beta _{6})q^{4}+\cdots\)
287.2.e.d \(34\) \(2.292\) None \(-3\) \(-1\) \(1\) \(-2\)