Space of modular forms of level 968, weight 2, and Character 968.k

• Label: 968.2.k
• Level: $968$
• Weight: $2$
• Character orbit: 968.k
• Rep. character: $\chi_{968}(403,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $400$
• Newform subspaces: $11$
• Sturm bound: $264$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.k (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 88 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(264\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(3\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

	Total	New	Old
Modular forms	576	464	112
Cusp forms	480	400	80
Eisenstein series	96	64	32

Trace form

\( 400 q + 5 q^{2} + 6 q^{3} + q^{4} + 5 q^{6} + 5 q^{8} - 78 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
968.2.k.a	$968$	$2$	968.k	88.k	$10$	$8$	$2$	$7.730$	8.0.64000000.1	\(\Q(\sqrt{-2}) \)			88.2.g.a	$16$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-\beta _{7}q^{2}-2\beta _{6}q^{3}-2\beta _{4}q^{4}-2\beta _{3}q^{6}+\cdots\)
968.2.k.b	$968$	$2$	968.k	88.k	$10$	$8$	$2$	$7.730$	8.0.64000000.1	\(\Q(\sqrt{-2}) \)			88.2.k.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}-\beta _{6}+\beta _{7})q^{3}+\cdots\)
968.2.k.c	$968$	$2$	968.k	88.k	$10$	$8$	$2$	$7.730$	8.0.64000000.1	\(\Q(\sqrt{-2}) \)			88.2.k.a	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q+\beta _{3}q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots\)
968.2.k.d	$968$	$2$	968.k	88.k	$10$	$8$	$2$	$7.730$	8.0.64000000.1	\(\Q(\sqrt{-2}) \)			88.2.k.a	$4$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{10}]$	\(q-\beta _{3}q^{2}+(\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{3}+\cdots\)
968.2.k.e	$968$	$2$	968.k	88.k	$10$	$32$	$8$	$7.730$		None			88.2.k.b	$4$	$0$	\(-5\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
968.2.k.f	$968$	$2$	968.k	88.k	$10$	$32$	$8$	$7.730$		None		✓	968.2.g.b	$16$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
968.2.k.g	$968$	$2$	968.k	88.k	$10$	$32$	$8$	$7.730$		None			88.2.g.b	$16$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
968.2.k.h	$968$	$2$	968.k	88.k	$10$	$32$	$8$	$7.730$		None			88.2.k.b	$4$	$0$	\(5\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
968.2.k.i	$968$	$2$	968.k	88.k	$10$	$32$	$8$	$7.730$		None			88.2.k.b	$4$	$0$	\(5\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
968.2.k.j	$968$	$2$	968.k	88.k	$10$	$80$	$20$	$7.730$		None		✓	968.2.g.c	$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
968.2.k.k	$968$	$2$	968.k	88.k	$10$	$128$	$32$	$7.730$		None		✓	968.2.g.d	$16$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(968, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(968, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)