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Properties

Label 266.2.u
Level $266$
Weight $2$
Character orbit 266.u
Rep. character $\chi_{266}(43,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $60$
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.u (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
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 264 60 204
Cusp forms 216 60 156
Eisenstein series 48 0 48

Trace form

\( 60 q + 6 q^{3} + 6 q^{6} + 6 q^{8} + 6 q^{9} + O(q^{10}) \) \( 60 q + 6 q^{3} + 6 q^{6} + 6 q^{8} + 6 q^{9} - 36 q^{15} - 24 q^{17} - 12 q^{18} - 24 q^{22} + 6 q^{24} - 24 q^{25} - 6 q^{27} + 48 q^{29} - 12 q^{31} - 6 q^{33} + 12 q^{35} + 6 q^{36} - 24 q^{37} + 18 q^{38} + 96 q^{39} - 18 q^{41} + 24 q^{43} - 12 q^{44} - 36 q^{45} + 12 q^{46} - 60 q^{47} - 12 q^{48} - 30 q^{49} + 42 q^{50} - 42 q^{51} - 12 q^{53} - 18 q^{54} - 36 q^{55} - 24 q^{56} + 108 q^{57} - 48 q^{58} + 102 q^{59} - 96 q^{61} - 48 q^{62} - 48 q^{63} - 30 q^{64} - 12 q^{65} + 90 q^{66} - 6 q^{67} - 6 q^{68} - 36 q^{69} - 24 q^{70} + 60 q^{71} - 12 q^{72} + 12 q^{73} + 12 q^{74} + 12 q^{78} + 12 q^{79} - 54 q^{81} - 6 q^{82} + 12 q^{84} + 36 q^{85} + 24 q^{87} + 12 q^{88} - 12 q^{89} - 72 q^{90} - 60 q^{93} - 36 q^{95} + 6 q^{97} - 162 q^{99} + O(q^{100}) \)

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.u.a 266.u 19.e $6$ $2.124$ \(\Q(\zeta_{18})\) None \(0\) \(3\) \(6\) \(-3\) $\mathrm{SU}(2)[C_{9}]$ \(q-\zeta_{18}q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{3}+\cdots\)
266.2.u.b 266.u 19.e $12$ $2.124$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{8}+\beta _{9})q^{2}+(-\beta _{1}+\beta _{6}+\beta _{8})q^{3}+\cdots\)
266.2.u.c 266.u 19.e $18$ $2.124$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(3\) \(-6\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{9}+\beta _{12})q^{2}+(\beta _{5}+\beta _{7})q^{3}-\beta _{8}q^{4}+\cdots\)
266.2.u.d 266.u 19.e $24$ $2.124$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(266, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)