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Properties

Label 966.2.a
Level $966$
Weight $2$
Character orbit 966.a
Rep. character $\chi_{966}(1,\cdot)$
Character field $\Q$
Dimension $21$
Newform subspaces $16$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(966))\).

Total New Old
Modular forms 200 21 179
Cusp forms 185 21 164
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.

\(2\)\(3\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(+\)\(-\)\(-\)$+$\(2\)
\(+\)\(-\)\(+\)\(+\)$-$\(2\)
\(+\)\(-\)\(+\)\(-\)$+$\(1\)
\(+\)\(-\)\(-\)\(-\)$-$\(3\)
\(-\)\(+\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)$-$\(3\)
Plus space\(+\)\(5\)
Minus space\(-\)\(16\)

Trace form

\( 21 q - 3 q^{2} + q^{3} + 21 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 21 q^{9} + O(q^{10}) \) \( 21 q - 3 q^{2} + q^{3} + 21 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 21 q^{9} - 2 q^{10} + 12 q^{11} + q^{12} + 6 q^{13} + q^{14} + 6 q^{15} + 21 q^{16} + 10 q^{17} - 3 q^{18} + 20 q^{19} - 2 q^{20} + q^{21} + 12 q^{22} + q^{23} + q^{24} + 35 q^{25} - 10 q^{26} + q^{27} + q^{28} + 6 q^{29} + 6 q^{30} + 16 q^{31} - 3 q^{32} - 4 q^{33} - 6 q^{34} + 6 q^{35} + 21 q^{36} + 14 q^{37} + 20 q^{38} + 14 q^{39} - 2 q^{40} + 2 q^{41} + q^{42} + 12 q^{43} + 12 q^{44} - 2 q^{45} - 7 q^{46} + 16 q^{47} + q^{48} + 21 q^{49} - 13 q^{50} + 2 q^{51} + 6 q^{52} - 18 q^{53} + q^{54} - 24 q^{55} + q^{56} - 12 q^{57} + 14 q^{58} - 4 q^{59} + 6 q^{60} - 26 q^{61} + q^{63} + 21 q^{64} - 12 q^{65} + 12 q^{66} - 12 q^{67} + 10 q^{68} + q^{69} - 2 q^{70} - 8 q^{71} - 3 q^{72} + 2 q^{73} - 18 q^{74} - q^{75} + 20 q^{76} - 20 q^{77} + 6 q^{78} + 48 q^{79} - 2 q^{80} + 21 q^{81} + 2 q^{82} - 44 q^{83} + q^{84} - 36 q^{85} - 4 q^{86} - 2 q^{87} + 12 q^{88} - 14 q^{89} - 2 q^{90} + 14 q^{91} + q^{92} + 24 q^{93} - 32 q^{94} - 40 q^{95} + q^{96} + 26 q^{97} - 3 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(966))\) 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 3 7 23
966.2.a.a 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.b 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.c 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.d 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(3\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.e 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
966.2.a.f 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
966.2.a.g 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.h 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.i 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.j 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.k 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(1\) \(3\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.l 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(1\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.m 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(-1\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots\)
966.2.a.n 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.o 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(-3\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
966.2.a.p 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(4\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(966))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(966)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 2}\)