Space of modular forms of level 966, weight 6, and trivial character

• Label: 966.6.a
• Level: $966$
• Weight: $6$
• Character orbit: 966.a
• Rep. character: $\chi_{966}(1,\cdot)$
• Character field: $\Q$
• Dimension: $108$
• Newform subspaces: $18$
• Sturm bound: $1152$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1152\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(966))\).

	Total	New	Old
Modular forms	968	108	860
Cusp forms	952	108	844
Eisenstein series	16	0	16

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

\(2\)	\(3\)	\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(7\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(5\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(8\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(6\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(8\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(9\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(5\)
Plus space				\(+\)	\(48\)
Minus space				\(-\)	\(60\)

Trace form

\( 108 q + 16 q^{2} + 1728 q^{4} - 88 q^{5} + 256 q^{8} + 8748 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(966))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	7	23
966.6.a.a	$966$	$6$	966.a	1.a	$1$	$1$	$1$	$154.931$	\(\Q\)	None	✓	$1$	$1$	\(-4\)	\(-9\)	\(-54\)	\(49\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}-54q^{5}+6^{2}q^{6}+\cdots\)
966.6.a.b	$966$	$6$	966.a	1.a	$1$	$1$	$1$	$154.931$	\(\Q\)	None	✓	$1$	$1$	\(4\)	\(9\)	\(28\)	\(49\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+28q^{5}+6^{2}q^{6}+\cdots\)
966.6.a.c	$966$	$6$	966.a	1.a	$1$	$4$	$4$	$154.931$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(16\)	\(36\)	\(-178\)	\(196\)		$-$	$-$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+(-44-\beta _{1}+\cdots)q^{5}+\cdots\)
966.6.a.d	$966$	$6$	966.a	1.a	$1$	$5$	$5$	$154.931$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓	$1$	$1$	\(-20\)	\(45\)	\(14\)	\(245\)		$+$	$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
966.6.a.e	$966$	$6$	966.a	1.a	$1$	$6$	$6$	$154.931$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-24\)	\(-54\)	\(-36\)	\(-294\)		$+$	$+$	$+$	$+$	$+$	$2^{2}\cdot 5$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-6+\beta _{5})q^{5}+\cdots\)
966.6.a.f	$966$	$6$	966.a	1.a	$1$	$6$	$6$	$154.931$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-24\)	\(-54\)	\(18\)	\(294\)		$+$	$+$	$-$	$-$	$+$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(3+\beta _{1})q^{5}+\cdots\)
966.6.a.g	$966$	$6$	966.a	1.a	$1$	$6$	$6$	$154.931$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(-24\)	\(-54\)	\(89\)	\(294\)		$+$	$+$	$-$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(15-\beta _{2})q^{5}+\cdots\)
966.6.a.h	$966$	$6$	966.a	1.a	$1$	$6$	$6$	$154.931$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(-24\)	\(54\)	\(14\)	\(-294\)		$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(2+\beta _{1}+\beta _{4}+\cdots)q^{5}+\cdots\)
966.6.a.i	$966$	$6$	966.a	1.a	$1$	$6$	$6$	$154.931$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(24\)	\(-54\)	\(0\)	\(-294\)		$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+\beta _{2}q^{5}-6^{2}q^{6}+\cdots\)
966.6.a.j	$966$	$6$	966.a	1.a	$1$	$6$	$6$	$154.931$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(24\)	\(54\)	\(0\)	\(-294\)		$-$	$-$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+\beta _{5}q^{5}+6^{2}q^{6}+\cdots\)
966.6.a.k	$966$	$6$	966.a	1.a	$1$	$7$	$7$	$154.931$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-28\)	\(-63\)	\(39\)	\(-343\)		$+$	$+$	$+$	$-$	$-$	$2^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q-4q^{2}-9q^{3}+2^{4}q^{4}+(6-\beta _{1})q^{5}+\cdots\)
966.6.a.l	$966$	$6$	966.a	1.a	$1$	$7$	$7$	$154.931$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(-28\)	\(63\)	\(-11\)	\(-343\)		$+$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
966.6.a.m	$966$	$6$	966.a	1.a	$1$	$7$	$7$	$154.931$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(28\)	\(-63\)	\(-50\)	\(343\)		$-$	$+$	$-$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-7-\beta _{1}+\cdots)q^{5}+\cdots\)
966.6.a.n	$966$	$6$	966.a	1.a	$1$	$7$	$7$	$154.931$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(28\)	\(-63\)	\(25\)	\(343\)		$-$	$+$	$-$	$-$	$-$	$2^{2}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+(4-\beta _{1})q^{5}+\cdots\)
966.6.a.o	$966$	$6$	966.a	1.a	$1$	$8$	$8$	$154.931$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(-32\)	\(72\)	\(39\)	\(392\)		$+$	$-$	$-$	$-$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q-4q^{2}+9q^{3}+2^{4}q^{4}+(5-\beta _{1})q^{5}+\cdots\)
966.6.a.p	$966$	$6$	966.a	1.a	$1$	$8$	$8$	$154.931$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(-72\)	\(-75\)	\(-392\)		$-$	$+$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+4q^{2}-9q^{3}+2^{4}q^{4}+(-9-\beta _{1}+\cdots)q^{5}+\cdots\)
966.6.a.q	$966$	$6$	966.a	1.a	$1$	$8$	$8$	$154.931$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(32\)	\(72\)	\(25\)	\(-392\)		$-$	$-$	$+$	$-$	$-$	$2^{4}\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+(3+\beta _{1})q^{5}+\cdots\)
966.6.a.r	$966$	$6$	966.a	1.a	$1$	$9$	$9$	$154.931$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(36\)	\(81\)	\(25\)	\(441\)		$-$	$-$	$-$	$+$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+4q^{2}+9q^{3}+2^{4}q^{4}+(3-\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(966))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(966)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 2}\)