Properties

Label 66.2.a
Level 66
Weight 2
Character orbit a
Rep. character \(\chi_{66}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 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: \(\Q\)
Newforms: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(66))\) into irreducible Hecke orbits

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

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