Space of modular forms of level 968, weight 6, and trivial character

• Label: 968.6.a
• Level: $968$
• Weight: $6$
• Character orbit: 968.a
• Rep. character: $\chi_{968}(1,\cdot)$
• Character field: $\Q$
• Dimension: $136$
• Newform subspaces: $17$
• Sturm bound: $792$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	968.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(792\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(968))\).

	Total	New	Old
Modular forms	684	136	548
Cusp forms	636	136	500
Eisenstein series	48	0	48

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

\(2\)	\(11\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(32\)
\(+\)	\(-\)	$-$	\(36\)
\(-\)	\(+\)	$-$	\(34\)
\(-\)	\(-\)	$+$	\(34\)
Plus space		\(+\)	\(66\)
Minus space		\(-\)	\(70\)

Trace form

\( 136 q - 2 q^{3} - 74 q^{5} - 100 q^{7} + 11158 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(968))\) 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	11
968.6.a.a	$968$	$6$	968.a	1.a	$1$	$1$	$1$	$155.252$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(20\)	\(-74\)	\(24\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+20q^{3}-74q^{5}+24q^{7}+157q^{9}+\cdots\)
968.6.a.b	$968$	$6$	968.a	1.a	$1$	$2$	$2$	$155.252$	\(\Q(\sqrt{37}) \)	None	✓	$1$	$0$	\(0\)	\(-14\)	\(18\)	\(-48\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-7-\beta )q^{3}+9q^{5}+(-24-11\beta )q^{7}+\cdots\)
968.6.a.c	$968$	$6$	968.a	1.a	$1$	$3$	$3$	$155.252$	3.3.1784453.1	None	✓	$1$	$1$	\(0\)	\(14\)	\(56\)	\(-112\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(5-\beta _{2})q^{3}+(19+\beta _{1}-\beta _{2})q^{5}+(-38+\cdots)q^{7}+\cdots\)
968.6.a.d	$968$	$6$	968.a	1.a	$1$	$4$	$4$	$155.252$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-13\)	\(-19\)	\(-58\)		$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-3-\beta _{1})q^{3}+(-5+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
968.6.a.e	$968$	$6$	968.a	1.a	$1$	$4$	$4$	$155.252$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-5\)	\(93\)	\(94\)		$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(24-2\beta _{1}-\beta _{3})q^{5}+\cdots\)
968.6.a.f	$968$	$6$	968.a	1.a	$1$	$6$	$6$	$155.252$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-18\)	\(-124\)		$-$	$-$	$+$	$2^{11}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-3+\beta _{3})q^{5}+(-20+\cdots)q^{7}+\cdots\)
968.6.a.g	$968$	$6$	968.a	1.a	$1$	$6$	$6$	$155.252$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-4\)	\(-18\)	\(124\)		$+$	$-$	$-$	$2^{11}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(-3+\beta _{3})q^{5}+(20+\cdots)q^{7}+\cdots\)
968.6.a.h	$968$	$6$	968.a	1.a	$1$	$6$	$6$	$155.252$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(9\)	\(-33\)	\(-88\)		$+$	$+$	$+$	$2^{9}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+(-5-\beta _{2})q^{5}+(-2^{4}+\cdots)q^{7}+\cdots\)
968.6.a.i	$968$	$6$	968.a	1.a	$1$	$6$	$6$	$155.252$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(9\)	\(-33\)	\(88\)		$-$	$+$	$-$	$2^{9}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+(-5-\beta _{2})q^{5}+(2^{4}-\beta _{1}+\cdots)q^{7}+\cdots\)
968.6.a.j	$968$	$6$	968.a	1.a	$1$	$7$	$7$	$155.252$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-14\)	\(19\)	\(-62\)		$-$	$-$	$+$	$2^{17}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{3}+(3-\beta _{2})q^{5}+(-9+\cdots)q^{7}+\cdots\)
968.6.a.k	$968$	$6$	968.a	1.a	$1$	$7$	$7$	$155.252$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-14\)	\(19\)	\(62\)		$+$	$-$	$-$	$2^{17}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{3}+(3-\beta _{2})q^{5}+(9-2\beta _{1}+\cdots)q^{7}+\cdots\)
968.6.a.l	$968$	$6$	968.a	1.a	$1$	$12$	$12$	$155.252$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(18\)	\(-42\)	\(-206\)		$+$	$+$	$+$	$2^{18}\cdot 3\cdot 11^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-3-\beta _{6})q^{5}+(-18+\cdots)q^{7}+\cdots\)
968.6.a.m	$968$	$6$	968.a	1.a	$1$	$12$	$12$	$155.252$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(18\)	\(-42\)	\(206\)		$-$	$+$	$-$	$2^{18}\cdot 3\cdot 11^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(-3-\beta _{6})q^{5}+(18-\beta _{1}+\cdots)q^{7}+\cdots\)
968.6.a.n	$968$	$6$	968.a	1.a	$1$	$14$	$14$	$155.252$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-23\)	\(-81\)	\(-85\)		$+$	$+$	$+$	$2^{20}\cdot 11^{5}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-5-\beta _{1}+\beta _{7})q^{5}+\cdots\)
968.6.a.o	$968$	$6$	968.a	1.a	$1$	$14$	$14$	$155.252$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-23\)	\(-81\)	\(85\)		$-$	$-$	$+$	$2^{20}\cdot 11^{5}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+(-5-\beta _{1}+\beta _{7})q^{5}+\cdots\)
968.6.a.p	$968$	$6$	968.a	1.a	$1$	$16$	$16$	$155.252$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(12\)	\(81\)	\(-47\)		$+$	$-$	$-$	$2^{26}\cdot 11^{8}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(5-\beta _{5})q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
968.6.a.q	$968$	$6$	968.a	1.a	$1$	$16$	$16$	$155.252$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(12\)	\(81\)	\(47\)		$-$	$+$	$-$	$2^{26}\cdot 11^{8}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(5-\beta _{5})q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(968))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(968)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)