Space of modular forms of level 1176, weight 2, and Character 1176.c

• Label: 1176.2.c
• Level: $1176$
• Weight: $2$
• Character orbit: 1176.c
• Rep. character: $\chi_{1176}(589,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $7$
• Sturm bound: $448$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(448\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

	Total	New	Old
Modular forms	240	82	158
Cusp forms	208	82	126
Eisenstein series	32	0	32

Trace form

\( 82 q + 2 q^{2} - 4 q^{4} - 2 q^{6} - 4 q^{8} - 82 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1176.2.c.a	$1176$	$2$	1176.c	8.b	$2$	$2$	$2$	$9.390$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+2iq^{5}+\cdots\)
1176.2.c.b	$1176$	$2$	1176.c	8.b	$2$	$4$	$4$	$9.390$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(\zeta_{12}-2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1176.2.c.c	$1176$	$2$	1176.c	8.b	$2$	$8$	$8$	$9.390$	8.0.386672896.3	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
1176.2.c.d	$1176$	$2$	1176.c	8.b	$2$	$12$	$12$	$9.390$	12.0.\(\cdots\).1	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+\beta _{7}q^{3}-\beta _{11}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
1176.2.c.e	$1176$	$2$	1176.c	8.b	$2$	$16$	$16$	$9.390$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}-\beta _{4}q^{5}+\cdots\)
1176.2.c.f	$1176$	$2$	1176.c	8.b	$2$	$16$	$16$	$9.390$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{2}+\beta _{4}q^{3}-\beta _{3}q^{4}-\beta _{2}q^{5}+\cdots\)
1176.2.c.g	$1176$	$2$	1176.c	8.b	$2$	$24$	$24$	$9.390$		None		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \cong \)