Space of modular forms of level 968, weight 2, and trivial character

• Label: 968.2.a
• Level: $968$
• Weight: $2$
• Character orbit: 968.a
• Rep. character: $\chi_{968}(1,\cdot)$
• Character field: $\Q$
• Dimension: $27$
• Newform subspaces: $14$
• Sturm bound: $264$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(264\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(968))\).

	Total	New	Old
Modular forms	156	27	129
Cusp forms	109	27	82
Eisenstein series	47	0	47

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
\(+\)	\(+\)	$+$	\(5\)
\(+\)	\(-\)	$-$	\(9\)
\(-\)	\(+\)	$-$	\(7\)
\(-\)	\(-\)	$+$	\(6\)
Plus space		\(+\)	\(11\)
Minus space		\(-\)	\(16\)

Trace form

\( 27 q + 2 q^{3} + 4 q^{7} + 21 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(968))\) 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
968.2.a.a	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-3\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-3q^{5}+2q^{7}+6q^{9}+9q^{15}+\cdots\)
968.2.a.b	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-4q^{7}-3q^{9}-3q^{13}-3q^{17}+\cdots\)
968.2.a.c	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(3\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+4q^{7}-3q^{9}+3q^{13}+3q^{17}+\cdots\)
968.2.a.d	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots\)
968.2.a.e	$968$	$2$	968.a	1.a	$1$	$1$	$1$	$7.730$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}-2q^{9}+4q^{13}+\cdots\)
968.2.a.f	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(0\)	\(-2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+\beta q^{5}+(-1-\beta )q^{7}+\cdots\)
968.2.a.g	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+\beta q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
968.2.a.h	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}-\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
968.2.a.i	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
968.2.a.j	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
968.2.a.k	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-4\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
968.2.a.l	$968$	$2$	968.a	1.a	$1$	$2$	$2$	$7.730$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
968.2.a.m	$968$	$2$	968.a	1.a	$1$	$4$	$4$	$7.730$	4.4.5225.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
968.2.a.n	$968$	$2$	968.a	1.a	$1$	$4$	$4$	$7.730$	4.4.5225.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(968))\) into lower level spaces

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