Properties

Label 287.2.h
Level 287
Weight 2
Character orbit h
Rep. character \(\chi_{287}(57,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 88
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.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 41 \)
Character field: \(\Q(\zeta_{5})\)
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 120 88 32
Cusp forms 104 88 16
Eisenstein series 16 0 16

Trace form

\( 88q - 4q^{2} - 4q^{3} - 24q^{4} - 8q^{5} - 6q^{6} + 6q^{8} + 92q^{9} + O(q^{10}) \) \( 88q - 4q^{2} - 4q^{3} - 24q^{4} - 8q^{5} - 6q^{6} + 6q^{8} + 92q^{9} + 12q^{10} + 2q^{11} - 40q^{12} - 28q^{13} + 12q^{15} - 44q^{16} - 22q^{17} - 32q^{18} + 10q^{19} + 30q^{20} - 4q^{21} - 16q^{22} + 24q^{24} - 50q^{25} + 6q^{26} - 52q^{27} - 32q^{29} - 44q^{30} + 2q^{31} + 48q^{32} - 34q^{33} - 2q^{34} - 4q^{35} - 26q^{36} + 32q^{37} + 108q^{38} + 32q^{39} - 4q^{40} + 8q^{41} - 4q^{42} - 30q^{43} - 48q^{44} - 16q^{45} - 12q^{46} + 32q^{47} + 84q^{48} - 22q^{49} + 56q^{50} - 64q^{51} - 14q^{52} - 16q^{53} - 46q^{54} - 8q^{55} - 56q^{57} + 18q^{58} - 44q^{59} - 2q^{60} - 24q^{61} - 60q^{62} - 8q^{63} + 22q^{64} + 28q^{65} - 14q^{66} - 14q^{67} + 36q^{68} - 4q^{69} - 8q^{70} + 12q^{71} + 26q^{72} - 28q^{73} + 48q^{74} - 46q^{75} + 50q^{76} - 8q^{77} + 122q^{78} + 100q^{79} + 94q^{80} + 72q^{81} + 34q^{82} - 60q^{83} - 26q^{84} + 72q^{85} + 6q^{86} + 40q^{87} - 56q^{88} - 52q^{89} - 4q^{90} + 24q^{91} + 40q^{92} + 20q^{93} + 22q^{94} - 40q^{95} - 204q^{96} + 22q^{97} - 4q^{98} - 32q^{99} + O(q^{100}) \)

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.h.a \(4\) \(2.292\) \(\Q(\zeta_{10})\) None \(0\) \(0\) \(-1\) \(1\) \(q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots\)
287.2.h.b \(4\) \(2.292\) \(\Q(\zeta_{10})\) None \(1\) \(6\) \(-2\) \(-1\) \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
287.2.h.c \(40\) \(2.292\) None \(-3\) \(0\) \(-4\) \(-10\)
287.2.h.d \(40\) \(2.292\) None \(-2\) \(-10\) \(-1\) \(10\)

Decomposition of \(S_{2}^{\mathrm{old}}(287, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(287, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)