Space of modular forms of level 1183, weight 2, and trivial character

• Label: 1183.2.a
• Level: $1183$
• Weight: $2$
• Character orbit: 1183.a
• Rep. character: $\chi_{1183}(1,\cdot)$
• Character field: $\Q$
• Dimension: $77$
• Newform subspaces: $18$
• Sturm bound: $242$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(242\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1183))\).

	Total	New	Old
Modular forms	134	77	57
Cusp forms	107	77	30
Eisenstein series	27	0	27

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

\(7\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(17\)
\(+\)	\(-\)	\(-\)	\(21\)
\(-\)	\(+\)	\(-\)	\(24\)
\(-\)	\(-\)	\(+\)	\(15\)
Plus space		\(+\)	\(32\)
Minus space		\(-\)	\(45\)

Trace form

\( 77 q + q^{2} + 4 q^{3} + 81 q^{4} - 2 q^{5} + q^{7} - 3 q^{8} + 81 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	13
1183.2.a.a	$1183$	$2$	1183.a	1.a	$1$	$1$	$1$	$9.446$	\(\Q\)	None	✓				91.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+4q^{12}+\cdots\)
1183.2.a.b	$1183$	$2$	1183.a	1.a	$1$	$1$	$1$	$9.446$	\(\Q\)	None	✓				91.2.a.a	$1$	$0$	\(2\)	\(0\)	\(3\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+3q^{5}+q^{7}-3q^{9}+\cdots\)
1183.2.a.c	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	\(\Q(\sqrt{5}) \)	None	✓				91.2.f.a	$1$	$1$	\(-3\)	\(-3\)	\(-3\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.d	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	\(\Q(\sqrt{2}) \)	None	✓				91.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+\beta q^{3}+(-3+\beta )q^{5}+2q^{6}+\cdots\)
1183.2.a.e	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	\(\Q(\sqrt{3}) \)	None	✓				91.2.f.b	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-3+\cdots)q^{6}+\cdots\)
1183.2.a.f	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	\(\Q(\sqrt{3}) \)	None	✓				91.2.f.b	$1$	$0$	\(0\)	\(2\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
1183.2.a.g	$1183$	$2$	1183.a	1.a	$1$	$2$	$2$	$9.446$	\(\Q(\sqrt{5}) \)	None	✓				91.2.f.a	$1$	$0$	\(3\)	\(-3\)	\(3\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.h	$1183$	$2$	1183.a	1.a	$1$	$3$	$3$	$9.446$	3.3.148.1	None	✓				91.2.c.a	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.i	$1183$	$2$	1183.a	1.a	$1$	$3$	$3$	$9.446$	3.3.316.1	None	✓				91.2.a.d	$1$	$0$	\(-1\)	\(-2\)	\(-2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1183.2.a.j	$1183$	$2$	1183.a	1.a	$1$	$3$	$3$	$9.446$	3.3.148.1	None	✓				91.2.c.a	$1$	$0$	\(2\)	\(0\)	\(3\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.k	$1183$	$2$	1183.a	1.a	$1$	$4$	$4$	$9.446$	4.4.27004.1	None	✓				91.2.f.c	$1$	$1$	\(-1\)	\(1\)	\(-7\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.l	$1183$	$2$	1183.a	1.a	$1$	$4$	$4$	$9.446$	4.4.27004.1	None	✓				91.2.f.c	$1$	$0$	\(1\)	\(1\)	\(7\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.m	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.7674048.1	None	✓				91.2.q.a	$1$	$1$	\(-4\)	\(0\)	\(-6\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.n	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.1279733.1	None	✓	✓			1183.2.a.n	$1$	$1$	\(-2\)	\(-4\)	\(-2\)	\(6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
1183.2.a.o	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.1279733.1	None	✓	✓	✓		1183.2.a.n	$1$	$1$	\(2\)	\(-4\)	\(2\)	\(-6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1183.2.a.p	$1183$	$2$	1183.a	1.a	$1$	$6$	$6$	$9.446$	6.6.7674048.1	None	✓				91.2.q.a	$1$	$0$	\(4\)	\(0\)	\(6\)	\(-6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.q	$1183$	$2$	1183.a	1.a	$1$	$12$	$12$	$9.446$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		1183.2.a.q	$1$	$0$	\(-3\)	\(8\)	\(4\)	\(-12\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.2.a.r	$1183$	$2$	1183.a	1.a	$1$	$12$	$12$	$9.446$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	✓	✓		1183.2.a.q	$1$	$0$	\(3\)	\(8\)	\(-4\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1183))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1183)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 2}\)