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Properties

Label 287.2.l
Level $287$
Weight $2$
Character orbit 287.l
Rep. character $\chi_{287}(27,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $104$
Newform subspaces $1$
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.l (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
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 120 120 0
Cusp forms 104 104 0
Eisenstein series 16 16 0

Trace form

\( 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9} + O(q^{10}) \) \( 104 q - 8 q^{2} - 4 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{11} - 8 q^{14} - 32 q^{15} - 96 q^{16} - 16 q^{18} - 24 q^{21} + 24 q^{22} + 12 q^{28} - 16 q^{29} + 48 q^{30} - 72 q^{32} - 44 q^{35} + 56 q^{36} + 32 q^{37} - 8 q^{39} - 8 q^{42} - 32 q^{43} + 72 q^{44} - 88 q^{46} - 12 q^{49} + 80 q^{50} + 32 q^{51} - 8 q^{53} + 104 q^{56} - 32 q^{57} - 96 q^{58} + 112 q^{60} - 132 q^{63} + 80 q^{65} + 56 q^{67} + 148 q^{70} - 104 q^{71} + 32 q^{74} - 16 q^{77} - 168 q^{78} - 124 q^{84} + 8 q^{85} - 64 q^{88} + 8 q^{91} + 104 q^{92} - 64 q^{93} - 8 q^{95} - 8 q^{98} + 8 q^{99} + O(q^{100}) \)

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.l.a 287.l 287.l $104$ $2.292$ None \(-8\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$