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Properties

Label 266.2.f
Level $266$
Weight $2$
Character orbit 266.f
Rep. character $\chi_{266}(197,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $4$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 266 = 2 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 266.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(266, [\chi])\).

Total New Old
Modular forms 88 20 68
Cusp forms 72 20 52
Eisenstein series 16 0 16

Trace form

\( 20 q + 2 q^{2} - 2 q^{3} - 10 q^{4} - 2 q^{6} - 4 q^{8} - 12 q^{9} + O(q^{10}) \) \( 20 q + 2 q^{2} - 2 q^{3} - 10 q^{4} - 2 q^{6} - 4 q^{8} - 12 q^{9} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 4 q^{14} - 12 q^{15} - 10 q^{16} - 24 q^{18} + 18 q^{19} + 4 q^{21} - 6 q^{22} - 4 q^{23} - 2 q^{24} - 26 q^{25} + 8 q^{26} + 28 q^{27} + 4 q^{29} + 40 q^{30} - 16 q^{31} + 2 q^{32} - 30 q^{33} + 12 q^{34} - 4 q^{35} - 12 q^{36} + 8 q^{37} + 4 q^{38} - 32 q^{39} + 26 q^{41} + 12 q^{43} - 2 q^{44} + 24 q^{45} - 24 q^{46} + 12 q^{47} - 2 q^{48} + 20 q^{49} - 4 q^{50} - 28 q^{51} + 16 q^{52} + 8 q^{53} - 2 q^{54} - 4 q^{55} - 8 q^{56} - 28 q^{57} - 8 q^{58} - 10 q^{59} - 12 q^{60} - 8 q^{61} - 12 q^{62} + 20 q^{64} - 32 q^{65} - 18 q^{66} + 14 q^{67} + 56 q^{69} - 24 q^{71} + 12 q^{72} - 6 q^{73} + 28 q^{74} + 100 q^{75} + 18 q^{76} + 16 q^{77} + 16 q^{78} - 16 q^{79} - 34 q^{81} - 14 q^{82} - 44 q^{83} - 8 q^{84} - 4 q^{85} + 36 q^{86} + 32 q^{87} + 12 q^{88} - 28 q^{89} - 36 q^{90} + 4 q^{91} - 4 q^{92} + 20 q^{93} + 16 q^{94} + 12 q^{95} + 4 q^{96} - 38 q^{97} + 2 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(266, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
266.2.f.a 266.f 19.c $2$ $2.124$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
266.2.f.b 266.f 19.c $4$ $2.124$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(-1\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
266.2.f.c 266.f 19.c $6$ $2.124$ 6.0.591408.1 None \(-3\) \(-2\) \(1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
266.2.f.d 266.f 19.c $8$ $2.124$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(4\) \(1\) \(-1\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4})q^{2}+(-\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(266, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(266, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)