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Properties

Label 287.2.bb
Level $287$
Weight $2$
Character orbit 287.bb
Rep. character $\chi_{287}(6,\cdot)$
Character field $\Q(\zeta_{40})$
Dimension $416$
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.bb (of order \(40\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 287 \)
Character field: \(\Q(\zeta_{40})\)
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 480 480 0
Cusp forms 416 416 0
Eisenstein series 64 64 0

Trace form

\( 416 q - 32 q^{2} - 40 q^{4} - 16 q^{7} - 48 q^{8} - 48 q^{9} + O(q^{10}) \) \( 416 q - 32 q^{2} - 40 q^{4} - 16 q^{7} - 48 q^{8} - 48 q^{9} - 32 q^{11} - 12 q^{14} - 8 q^{15} + 56 q^{16} - 24 q^{18} + 4 q^{21} - 64 q^{22} - 40 q^{23} - 40 q^{25} - 32 q^{28} - 24 q^{29} - 8 q^{30} + 32 q^{32} - 16 q^{35} - 96 q^{36} + 48 q^{37} - 32 q^{39} - 192 q^{42} - 8 q^{43} + 128 q^{44} + 48 q^{46} - 48 q^{49} - 120 q^{50} + 48 q^{51} - 32 q^{53} - 124 q^{56} - 8 q^{57} + 56 q^{58} - 152 q^{60} + 112 q^{63} - 40 q^{64} - 120 q^{65} - 96 q^{67} + 32 q^{70} + 64 q^{71} - 40 q^{72} - 72 q^{74} + 76 q^{77} + 128 q^{78} - 40 q^{79} + 304 q^{84} - 48 q^{85} - 40 q^{86} + 24 q^{88} + 132 q^{91} - 144 q^{92} + 24 q^{93} - 32 q^{95} + 88 q^{98} - 48 q^{99} + O(q^{100}) \)

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.bb.a 287.bb 287.ab $416$ $2.292$ None \(-32\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{40}]$