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Properties

Label 286.2.r
Level $286$
Weight $2$
Character orbit 286.r
Rep. character $\chi_{286}(57,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $112$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 286 = 2 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 286.r (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(286, [\chi])\).

Total New Old
Modular forms 368 112 256
Cusp forms 304 112 192
Eisenstein series 64 0 64

Trace form

\( 112 q - 28 q^{9} + O(q^{10}) \) \( 112 q - 28 q^{9} - 28 q^{11} + 20 q^{13} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 4 q^{22} - 4 q^{26} + 48 q^{27} - 20 q^{29} - 28 q^{31} + 96 q^{33} - 16 q^{34} - 200 q^{35} + 24 q^{37} + 40 q^{39} - 20 q^{41} + 8 q^{44} - 64 q^{45} - 40 q^{46} - 28 q^{47} + 32 q^{53} - 8 q^{55} - 4 q^{58} - 36 q^{59} - 8 q^{60} - 80 q^{61} + 80 q^{63} + 96 q^{66} + 56 q^{67} + 20 q^{68} - 52 q^{70} - 100 q^{71} - 40 q^{72} + 60 q^{73} - 64 q^{78} - 80 q^{79} + 84 q^{81} - 80 q^{84} - 80 q^{85} + 48 q^{86} - 88 q^{89} + 72 q^{91} - 16 q^{92} + 24 q^{93} - 180 q^{94} + 12 q^{97} - 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(286, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
286.2.r.a 286.r 143.s $112$ $2.284$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(286, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(286, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)