Properties

Label 66.2.a
Level $66$
Weight $2$
Character orbit 66.a
Rep. character $\chi_{66}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 66.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(66))\).

Total New Old
Modular forms 16 3 13
Cusp forms 9 3 6
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.

\(2\)\(3\)\(11\)FrickeDim.
\(+\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 3 q^{9} + O(q^{10}) \) \( 3 q + q^{2} + q^{3} + 3 q^{4} - 2 q^{5} - q^{6} - 4 q^{7} + q^{8} + 3 q^{9} - 2 q^{10} - q^{11} + q^{12} - 6 q^{13} - 8 q^{14} - 6 q^{15} + 3 q^{16} - 6 q^{17} + q^{18} - 2 q^{20} + 4 q^{21} + q^{22} + 4 q^{23} - q^{24} + 5 q^{25} + 2 q^{26} + q^{27} - 4 q^{28} + 22 q^{29} - 6 q^{30} + q^{32} + q^{33} + 6 q^{34} + 3 q^{36} - 6 q^{37} + 8 q^{38} + 6 q^{39} - 2 q^{40} + 2 q^{41} + 16 q^{43} - q^{44} - 2 q^{45} - 8 q^{46} - 20 q^{47} + q^{48} + 3 q^{49} + 15 q^{50} - 10 q^{51} - 6 q^{52} + 6 q^{53} - q^{54} - 6 q^{55} - 8 q^{56} - 8 q^{57} + 10 q^{58} + 12 q^{59} - 6 q^{60} - 14 q^{61} - 16 q^{62} - 4 q^{63} + 3 q^{64} - 28 q^{65} + 3 q^{66} - 12 q^{67} - 6 q^{68} - 4 q^{69} - 4 q^{71} + q^{72} - 10 q^{73} + 14 q^{74} + 7 q^{75} + 14 q^{78} + 20 q^{79} - 2 q^{80} + 3 q^{81} - 10 q^{82} - 4 q^{83} + 4 q^{84} + 12 q^{85} + 10 q^{87} + q^{88} + 14 q^{89} - 2 q^{90} + 8 q^{91} + 4 q^{92} - 8 q^{94} + 8 q^{95} - q^{96} - 2 q^{97} + 9 q^{98} - q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(66))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 11
66.2.a.a \(1\) \(0.527\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
66.2.a.b \(1\) \(0.527\) \(\Q\) None \(1\) \(-1\) \(2\) \(-4\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-4q^{7}+\cdots\)
66.2.a.c \(1\) \(0.527\) \(\Q\) None \(1\) \(1\) \(-4\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(66))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(66)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)