Space of modular forms of level 1183, weight 2, and Character 1183.c

• Label: 1183.2.c
• Level: $1183$
• Weight: $2$
• Character orbit: 1183.c
• Rep. character: $\chi_{1183}(337,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $10$
• Sturm bound: $242$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(242\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1183, [\chi])\).

	Total	New	Old
Modular forms	134	78	56
Cusp forms	106	78	28
Eisenstein series	28	0	28

Trace form

\( 78 q - 80 q^{4} + 86 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1183, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1183.2.c.a	$1183$	$2$	1183.c	13.b	$2$	$2$	$2$	$9.446$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+2q^{4}-3iq^{5}-iq^{7}+q^{9}+\cdots\)
1183.2.c.b	$1183$	$2$	1183.c	13.b	$2$	$2$	$2$	$9.446$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}+3iq^{5}-iq^{7}-3q^{9}+\cdots\)
1183.2.c.c	$1183$	$2$	1183.c	13.b	$2$	$4$	$4$	$9.446$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
1183.2.c.d	$1183$	$2$	1183.c	13.b	$2$	$4$	$4$	$9.446$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}+(3\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
1183.2.c.e	$1183$	$2$	1183.c	13.b	$2$	$4$	$4$	$9.446$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}^{3})q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1183.2.c.f	$1183$	$2$	1183.c	13.b	$2$	$6$	$6$	$9.446$	6.0.399424.1	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1183.2.c.g	$1183$	$2$	1183.c	13.b	$2$	$8$	$8$	$9.446$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
1183.2.c.h	$1183$	$2$	1183.c	13.b	$2$	$12$	$12$	$9.446$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{8}+\beta _{10}-\beta _{11})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots\)
1183.2.c.i	$1183$	$2$	1183.c	13.b	$2$	$12$	$12$	$9.446$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{7})q^{2}-\beta _{2}q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
1183.2.c.j	$1183$	$2$	1183.c	13.b	$2$	$24$	$24$	$9.446$		None		$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1183, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1183, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)