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.

\(2\)\(3\)\(7\)\(23\)FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)\(1\)\(7\)\(8\)\(1\)\(7\)\(0\)\(0\)\(0\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(15\)\(2\)\(13\)\(14\)\(2\)\(12\)\(1\)\(0\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(15\)\(1\)\(14\)\(14\)\(1\)\(13\)\(1\)\(0\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(12\)\(2\)\(10\)\(11\)\(2\)\(9\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(14\)\(2\)\(12\)\(13\)\(2\)\(11\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(11\)\(1\)\(10\)\(10\)\(1\)\(9\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(13\)\(0\)\(13\)\(12\)\(0\)\(12\)\(1\)\(0\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(12\)\(3\)\(9\)\(11\)\(3\)\(8\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(12\)\(2\)\(10\)\(11\)\(2\)\(9\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(14\)\(0\)\(14\)\(13\)\(0\)\(13\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(13\)\(1\)\(12\)\(12\)\(1\)\(11\)\(1\)\(0\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(11\)\(1\)\(10\)\(10\)\(1\)\(9\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(12\)\(0\)\(12\)\(11\)\(0\)\(11\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(14\)\(2\)\(12\)\(13\)\(2\)\(11\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(13\)\(3\)\(10\)\(12\)\(3\)\(9\)\(1\)\(0\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(11\)\(0\)\(11\)\(10\)\(0\)\(10\)\(1\)\(0\)\(1\)
Plus space\(+\)\(94\)\(5\)\(89\)\(87\)\(5\)\(82\)\(7\)\(0\)\(7\)
Minus space\(-\)\(106\)\(16\)\(90\)\(98\)\(16\)\(82\)\(8\)\(0\)\(8\)

Trace form

\( 21 q - 3 q^{2} + q^{3} + 21 q^{4} - 2 q^{5} + q^{6} + q^{7} - 3 q^{8} + 21 q^{9} - 2 q^{10} + 12 q^{11} + q^{12} + 6 q^{13} + q^{14} + 6 q^{15} + 21 q^{16} + 10 q^{17} - 3 q^{18} + 20 q^{19} - 2 q^{20}+ \cdots + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(966))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist 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 966.2.a.a \(-1\) \(-1\) \(-4\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.b 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.b \(-1\) \(-1\) \(-2\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.c 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.c \(-1\) \(-1\) \(2\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.d 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.d \(-1\) \(-1\) \(3\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.e 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.e \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
966.2.a.f 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.f \(-1\) \(1\) \(0\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
966.2.a.g 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.g \(1\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.h 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.h \(1\) \(-1\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.i 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.i \(1\) \(1\) \(-3\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.j 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.j \(1\) \(1\) \(-2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.k 966.a 1.a $1$ $7.714$ \(\Q\) None 966.2.a.k \(1\) \(1\) \(3\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.l 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{17}) \) None 966.2.a.l \(-2\) \(-2\) \(1\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.m 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{41}) \) None 966.2.a.m \(-2\) \(2\) \(-1\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots\)
966.2.a.n 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{41}) \) None 966.2.a.n \(-2\) \(2\) \(1\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.o 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{33}) \) None 966.2.a.o \(2\) \(-2\) \(-3\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
966.2.a.p 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{5}) \) None 966.2.a.p \(2\) \(2\) \(4\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)

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

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