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Properties

Label 286.2.b
Level $286$
Weight $2$
Character orbit 286.b
Rep. character $\chi_{286}(155,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $4$
Sturm bound $84$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 286 = 2 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 286.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(84\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 46 10 36
Cusp forms 38 10 28
Eisenstein series 8 0 8

Trace form

\( 10 q + 4 q^{3} - 10 q^{4} + 6 q^{9} + O(q^{10}) \) \( 10 q + 4 q^{3} - 10 q^{4} + 6 q^{9} - 8 q^{10} - 4 q^{12} + 4 q^{13} + 8 q^{14} + 10 q^{16} + 2 q^{22} + 20 q^{23} + 18 q^{25} + 2 q^{26} + 4 q^{27} - 16 q^{29} - 4 q^{30} - 20 q^{35} - 6 q^{36} - 8 q^{38} - 32 q^{39} + 8 q^{40} - 28 q^{42} - 8 q^{43} + 4 q^{48} - 34 q^{49} + 4 q^{51} - 4 q^{52} + 20 q^{53} - 8 q^{56} + 40 q^{61} + 36 q^{62} - 10 q^{64} - 24 q^{65} + 8 q^{66} - 64 q^{69} + 16 q^{74} + 16 q^{75} - 8 q^{77} - 4 q^{78} + 48 q^{79} + 26 q^{81} + 16 q^{82} + 8 q^{87} - 2 q^{88} - 12 q^{90} + 12 q^{91} - 20 q^{92} + 24 q^{94} + O(q^{100}) \)

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.b.a 286.b 13.b $2$ $2.284$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+3iq^{5}+iq^{7}-iq^{8}+\cdots\)
286.2.b.b 286.b 13.b $2$ $2.284$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-2iq^{5}-4iq^{7}-iq^{8}+\cdots\)
286.2.b.c 286.b 13.b $2$ $2.284$ \(\Q(\sqrt{-1}) \) None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3q^{3}-q^{4}+iq^{5}+3iq^{6}+\cdots\)
286.2.b.d 286.b 13.b $4$ $2.284$ \(\Q(i, \sqrt{17})\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{3})q^{3}-q^{4}+\beta _{2}q^{5}+\cdots\)

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

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