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Properties

Label 287.2.h
Level $287$
Weight $2$
Character orbit 287.h
Rep. character $\chi_{287}(57,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $88$
Newform subspaces $4$
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: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(287, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
287.2.h.a 287.h 41.d $4$ $2.292$ \(\Q(\zeta_{10})\) None \(0\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+2\zeta_{10}^{3}q^{4}+\cdots\)
287.2.h.b 287.h 41.d $4$ $2.292$ \(\Q(\zeta_{10})\) None \(1\) \(6\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+2\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
287.2.h.c 287.h 41.d $40$ $2.292$ None \(-3\) \(0\) \(-4\) \(-10\) $\mathrm{SU}(2)[C_{5}]$
287.2.h.d 287.h 41.d $40$ $2.292$ None \(-2\) \(-10\) \(-1\) \(10\) $\mathrm{SU}(2)[C_{5}]$

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

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