Properties

Label 266.2.a
Level $266$
Weight $2$
Character orbit 266.a
Rep. character $\chi_{266}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $4$
Sturm bound $80$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 266 = 2 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 266.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(266))\).

Total New Old
Modular forms 44 9 35
Cusp forms 37 9 28
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(19\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(0\)
Minus space\(-\)\(9\)

Trace form

\( 9 q + q^{2} + 4 q^{3} + 9 q^{4} + 6 q^{5} - 4 q^{6} - q^{7} + q^{8} + 17 q^{9} + O(q^{10}) \) \( 9 q + q^{2} + 4 q^{3} + 9 q^{4} + 6 q^{5} - 4 q^{6} - q^{7} + q^{8} + 17 q^{9} + 6 q^{10} + 8 q^{11} + 4 q^{12} + 6 q^{13} - q^{14} + 9 q^{16} - 6 q^{17} - 3 q^{18} - q^{19} + 6 q^{20} + 4 q^{21} - 12 q^{22} - 8 q^{23} - 4 q^{24} + 19 q^{25} - 2 q^{26} - 8 q^{27} - q^{28} - 10 q^{29} - 16 q^{30} + 32 q^{31} + q^{32} - 24 q^{33} + 18 q^{34} - 2 q^{35} + 17 q^{36} + 14 q^{37} - q^{38} - 24 q^{39} + 6 q^{40} - 14 q^{41} - 8 q^{43} + 8 q^{44} - 18 q^{45} - 24 q^{47} + 4 q^{48} + 9 q^{49} - 17 q^{50} - 32 q^{51} + 6 q^{52} - 26 q^{53} - 40 q^{54} - 32 q^{55} - q^{56} + 2 q^{58} - 20 q^{59} + 6 q^{61} - 24 q^{62} - 13 q^{63} + 9 q^{64} - 52 q^{65} - 24 q^{66} - 4 q^{67} - 6 q^{68} - 32 q^{69} - 6 q^{70} - 3 q^{72} + 10 q^{73} + 2 q^{74} + 4 q^{75} - q^{76} - 4 q^{77} + 8 q^{78} + 32 q^{79} + 6 q^{80} + 33 q^{81} + 2 q^{82} - 4 q^{83} + 4 q^{84} + 4 q^{85} - 12 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} + 6 q^{90} + 18 q^{91} - 8 q^{92} + 8 q^{93} + 8 q^{94} - 6 q^{95} - 4 q^{96} + 42 q^{97} + q^{98} + 56 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(266))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 19
266.2.a.a 266.a 1.a $2$ $2.124$ \(\Q(\sqrt{29}) \) None \(-2\) \(1\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
266.2.a.b 266.a 1.a $2$ $2.124$ \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\)
266.2.a.c 266.a 1.a $2$ $2.124$ \(\Q(\sqrt{13}) \) None \(2\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
266.2.a.d 266.a 1.a $3$ $2.124$ 3.3.469.1 None \(3\) \(-1\) \(5\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(266))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(266)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)