Properties

Label 287.2.r
Level 287
Weight 2
Character orbit r
Rep. character \(\chi_{287}(9,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 104
Newforms 3
Sturm bound 56
Trace bound 3

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Defining parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.r (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 287 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 3 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

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

\( 104q - 2q^{3} + 44q^{4} - 24q^{6} - 4q^{7} + O(q^{10}) \) \( 104q - 2q^{3} + 44q^{4} - 24q^{6} - 4q^{7} - 28q^{10} + 2q^{11} + 14q^{12} - 8q^{13} + 10q^{14} - 8q^{15} - 36q^{16} - 8q^{17} - 20q^{18} - 6q^{19} - 8q^{22} - 4q^{23} - 36q^{24} + 32q^{25} + 8q^{26} - 8q^{27} - 28q^{28} - 32q^{29} + 8q^{30} + 28q^{31} + 16q^{34} + 2q^{35} - 16q^{38} + 80q^{40} - 56q^{41} - 72q^{42} + 6q^{44} - 4q^{45} + 18q^{47} - 20q^{48} - 32q^{51} + 10q^{52} - 8q^{53} + 18q^{54} - 24q^{55} + 6q^{56} + 72q^{57} + 4q^{58} - 44q^{59} + 48q^{60} + 10q^{63} - 72q^{64} - 12q^{65} + 68q^{66} + 14q^{67} - 18q^{68} + 16q^{69} - 22q^{70} - 8q^{71} + 100q^{72} - 58q^{75} - 88q^{76} - 120q^{78} - 20q^{79} - 40q^{81} - 6q^{82} + 48q^{83} - 116q^{85} + 44q^{86} + 20q^{89} - 128q^{92} - 74q^{93} + 100q^{94} + 42q^{95} + 14q^{96} + 44q^{97} - 116q^{98} - 96q^{99} + O(q^{100}) \)

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.r.a \(4\) \(2.292\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(-6\) \(10\) \(q+\zeta_{12}q^{2}+(-1+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
287.2.r.b \(4\) \(2.292\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(6\) \(0\) \(q+\zeta_{12}q^{2}+(1+\zeta_{12})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
287.2.r.c \(96\) \(2.292\) None \(0\) \(-4\) \(0\) \(-14\)