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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 19
266.2.a.a \(2\) \(2.124\) \(\Q(\sqrt{29}) \) None \(-2\) \(1\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{2}+(1-\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
266.2.a.b \(2\) \(2.124\) \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(1\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+(1+\beta )q^{3}+q^{4}+(2-3\beta )q^{5}+\cdots\)
266.2.a.c \(2\) \(2.124\) \(\Q(\sqrt{13}) \) None \(2\) \(1\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
266.2.a.d \(3\) \(2.124\) 3.3.469.1 None \(3\) \(-1\) \(5\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)

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

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