Properties

Label 287.2.z
Level 287
Weight 2
Character orbit z
Rep. character \(\chi_{287}(4,\cdot)\)
Character field \(\Q(\zeta_{30})\)
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.z (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 208q - 3q^{2} + 21q^{4} + q^{5} - 40q^{6} - 10q^{7} - 8q^{8} + 84q^{9} + O(q^{10}) \) \( 208q - 3q^{2} + 21q^{4} + q^{5} - 40q^{6} - 10q^{7} - 8q^{8} + 84q^{9} - 6q^{10} - 5q^{11} - 35q^{12} - 20q^{13} - 50q^{15} + 21q^{16} - 5q^{17} + 18q^{18} - 5q^{19} - 96q^{20} + 8q^{21} + 20q^{22} + 40q^{24} + 27q^{25} - 5q^{26} + 5q^{28} + 20q^{29} - 45q^{30} - 11q^{31} - 30q^{32} - 10q^{33} + 100q^{34} - 106q^{36} - 16q^{37} - 4q^{39} + 6q^{40} - 14q^{41} - 8q^{42} - 8q^{43} + 34q^{45} - 32q^{46} + 25q^{47} - 50q^{48} + 14q^{49} - 120q^{50} + 2q^{51} - 105q^{52} + 20q^{53} - 35q^{54} + 100q^{56} - 98q^{57} - 5q^{58} - 37q^{59} - 100q^{60} + 51q^{61} - 70q^{62} - 30q^{63} - 100q^{64} + 40q^{65} - 176q^{66} + 15q^{67} - 30q^{69} + 105q^{70} - 10q^{71} - 33q^{72} - 34q^{73} - 23q^{74} - 120q^{75} + 110q^{76} + 72q^{77} - 18q^{78} + 127q^{80} - 24q^{81} - 63q^{82} - 128q^{83} + 33q^{84} - 61q^{86} + 28q^{87} + 150q^{88} + 35q^{89} - 34q^{90} + 14q^{91} + 102q^{92} - 55q^{93} - 155q^{94} + 55q^{95} + 20q^{97} + 88q^{98} + 120q^{99} + O(q^{100}) \)

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.z.a \(208\) \(2.292\) None \(-3\) \(0\) \(1\) \(-10\)