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Properties

Label 286.2.j
Level $286$
Weight $2$
Character orbit 286.j
Rep. character $\chi_{286}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $2$
Sturm bound $84$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 286 = 2 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 286.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(84\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 92 28 64
Cusp forms 76 28 48
Eisenstein series 16 0 16

Trace form

\( 28 q + 14 q^{4} - 22 q^{9} + O(q^{10}) \) \( 28 q + 14 q^{4} - 22 q^{9} - 4 q^{10} + 12 q^{13} + 16 q^{14} - 14 q^{16} + 12 q^{19} - 2 q^{22} - 2 q^{23} - 44 q^{25} - 2 q^{26} - 24 q^{27} + 4 q^{29} - 20 q^{30} + 20 q^{35} + 22 q^{36} - 28 q^{38} - 20 q^{39} - 8 q^{40} - 36 q^{41} - 8 q^{42} - 12 q^{43} + 60 q^{45} + 24 q^{46} + 30 q^{49} + 32 q^{51} + 12 q^{52} - 8 q^{53} + 36 q^{54} + 8 q^{56} - 6 q^{58} + 48 q^{59} - 8 q^{61} - 108 q^{63} - 28 q^{64} + 72 q^{65} + 16 q^{66} + 24 q^{67} - 8 q^{69} - 18 q^{71} - 24 q^{72} + 8 q^{74} + 4 q^{75} + 12 q^{76} - 16 q^{77} - 20 q^{78} - 40 q^{79} - 78 q^{81} + 8 q^{82} - 24 q^{84} - 44 q^{87} + 2 q^{88} - 54 q^{89} + 48 q^{90} + 60 q^{91} - 4 q^{92} + 24 q^{93} + 24 q^{94} - 24 q^{95} - 90 q^{97} - 24 q^{98} + O(q^{100}) \)

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.j.a 286.j 13.e $12$ $2.284$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{6}q^{2}+(\beta _{1}+\beta _{2}+\beta _{4}+2\beta _{5}+2\beta _{7}+\cdots)q^{3}+\cdots\)
286.2.j.b 286.j 13.e $16$ $2.284$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{11}q^{2}+(-\beta _{2}-\beta _{13})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(286, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)