Properties

Label 666.2.a
Level $666$
Weight $2$
Character orbit 666.a
Rep. character $\chi_{666}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $11$
Sturm bound $228$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(228\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(666))\).

Total New Old
Modular forms 122 15 107
Cusp forms 107 15 92
Eisenstein series 15 0 15

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

\(2\)\(3\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(5\)
Minus space\(-\)\(10\)

Trace form

\( 15 q + q^{2} + 15 q^{4} - 2 q^{5} + q^{8} + O(q^{10}) \) \( 15 q + q^{2} + 15 q^{4} - 2 q^{5} + q^{8} + 4 q^{10} + 2 q^{11} + 2 q^{13} + 4 q^{14} + 15 q^{16} + 6 q^{17} - 2 q^{20} - 8 q^{22} - 12 q^{23} + 15 q^{25} + 4 q^{26} + 6 q^{29} - 4 q^{31} + q^{32} - 6 q^{34} + 20 q^{35} - q^{37} + 4 q^{38} + 4 q^{40} - 4 q^{41} - 8 q^{43} + 2 q^{44} - 6 q^{46} - 4 q^{47} - 9 q^{49} + 15 q^{50} + 2 q^{52} + 14 q^{53} + 4 q^{55} + 4 q^{56} + 4 q^{58} + 20 q^{59} - 30 q^{61} - 18 q^{62} + 15 q^{64} + 40 q^{65} + 14 q^{67} + 6 q^{68} + 4 q^{70} + 28 q^{73} + 5 q^{74} - 28 q^{77} - 28 q^{79} - 2 q^{80} + 14 q^{82} - 4 q^{83} + 12 q^{85} - 8 q^{86} - 8 q^{88} + 10 q^{89} - 16 q^{91} - 12 q^{92} - 52 q^{95} + 10 q^{97} + 9 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(666))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 37
666.2.a.a \(1\) \(5.318\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots\)
666.2.a.b \(1\) \(5.318\) \(\Q\) None \(-1\) \(0\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+3q^{7}-q^{8}-q^{11}+q^{13}+\cdots\)
666.2.a.c \(1\) \(5.318\) \(\Q\) None \(-1\) \(0\) \(2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+2q^{5}-3q^{7}-q^{8}-2q^{10}+\cdots\)
666.2.a.d \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-4q^{5}-q^{7}+q^{8}-4q^{10}+\cdots\)
666.2.a.e \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(-2\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-2q^{5}-3q^{7}+q^{8}-2q^{10}+\cdots\)
666.2.a.f \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}+4q^{11}+\cdots\)
666.2.a.g \(1\) \(5.318\) \(\Q\) None \(1\) \(0\) \(4\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+4q^{5}+3q^{7}+q^{8}+4q^{10}+\cdots\)
666.2.a.h \(2\) \(5.318\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(-4\) \(1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+(1-\beta )q^{7}-q^{8}+\cdots\)
666.2.a.i \(2\) \(5.318\) \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(1-3\beta )q^{5}-2\beta q^{7}-q^{8}+\cdots\)
666.2.a.j \(2\) \(5.318\) \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(1\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+(2-2\beta )q^{7}+q^{8}+\cdots\)
666.2.a.k \(2\) \(5.318\) \(\Q(\sqrt{17}) \) None \(2\) \(0\) \(4\) \(1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+2q^{5}+(1-\beta )q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(666))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(666)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 2}\)