Space of modular forms of level 1149, weight 2, and trivial character

• Label: 1149.2.a
• Level: $1149$
• Weight: $2$
• Character orbit: 1149.a
• Rep. character: $\chi_{1149}(1,\cdot)$
• Character field: $\Q$
• Dimension: $63$
• Newform subspaces: $7$
• Sturm bound: $256$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1149 = 3 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1149.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(256\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1149))\).

	Total	New	Old
Modular forms	130	63	67
Cusp forms	127	63	64
Eisenstein series	3	0	3

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

\(3\)	\(383\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(14\)
\(+\)	\(-\)	$-$	\(18\)
\(-\)	\(+\)	$-$	\(17\)
\(-\)	\(-\)	$+$	\(14\)
Plus space		\(+\)	\(28\)
Minus space		\(-\)	\(35\)

Trace form

\( 63 q - 3 q^{2} - q^{3} + 61 q^{4} - 6 q^{5} + q^{6} - 8 q^{7} - 15 q^{8} + 63 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1149))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	383
1149.2.a.a	$1149$	$2$	1149.a	1.a	$1$	$1$	$1$	$9.175$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}+3q^{5}-4q^{7}+q^{9}-q^{11}+\cdots\)
1149.2.a.b	$1149$	$2$	1149.a	1.a	$1$	$1$	$1$	$9.175$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-3q^{5}+q^{9}+5q^{11}+\cdots\)
1149.2.a.c	$1149$	$2$	1149.a	1.a	$1$	$2$	$2$	$9.175$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(-1\)	\(-2\)	\(-6\)	\(6\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}-3q^{5}+\cdots\)
1149.2.a.d	$1149$	$2$	1149.a	1.a	$1$	$13$	$13$	$9.175$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-9\)	\(13\)	\(-9\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+q^{3}+(3-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1149.2.a.e	$1149$	$2$	1149.a	1.a	$1$	$13$	$13$	$9.175$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(1\)	\(-13\)	\(-5\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
1149.2.a.f	$1149$	$2$	1149.a	1.a	$1$	$16$	$16$	$9.175$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	✓	$1$	$0$	\(-2\)	\(-16\)	\(6\)	\(2\)		$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+\cdots\)
1149.2.a.g	$1149$	$2$	1149.a	1.a	$1$	$17$	$17$	$9.175$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(8\)	\(17\)	\(8\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1149))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1149)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(383))\)\(^{\oplus 2}\)