Space of modular forms of level 1147, weight 2, and trivial character

• Label: 1147.2.a
• Level: $1147$
• Weight: $2$
• Character orbit: 1147.a
• Rep. character: $\chi_{1147}(1,\cdot)$
• Character field: $\Q$
• Dimension: $91$
• Newform subspaces: $9$
• Sturm bound: $202$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1147 = 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1147.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(202\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1147))\).

	Total	New	Old
Modular forms	102	91	11
Cusp forms	99	91	8
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.

\(31\)	\(37\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(-\)	$-$	\(27\)
\(-\)	\(+\)	$-$	\(24\)
\(-\)	\(-\)	$+$	\(19\)
Plus space		\(+\)	\(40\)
Minus space		\(-\)	\(51\)

Trace form

\( 91 q + q^{2} + 97 q^{4} - 2 q^{5} + 4 q^{7} + 3 q^{8} + 75 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1147))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		31	37
1147.2.a.a	$1147$	$2$	1147.a	1.a	$1$	$1$	$1$	$9.159$	\(\Q\)	None	✓	$1$	$1$	\(-2\)	\(-1\)	\(-4\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+2q^{4}-4q^{5}+2q^{6}+\cdots\)
1147.2.a.b	$1147$	$2$	1147.a	1.a	$1$	$1$	$1$	$9.159$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(-5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-2q^{5}-5q^{7}-2q^{9}+\cdots\)
1147.2.a.c	$1147$	$2$	1147.a	1.a	$1$	$2$	$2$	$9.159$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-3\)	\(-4\)	\(0\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}-2q^{3}+3\beta q^{4}+(1-2\beta )q^{5}+\cdots\)
1147.2.a.d	$1147$	$2$	1147.a	1.a	$1$	$3$	$3$	$9.159$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
1147.2.a.e	$1147$	$2$	1147.a	1.a	$1$	$4$	$4$	$9.159$	4.4.1957.1	None	✓	$1$	$1$	\(1\)	\(-4\)	\(-7\)	\(5\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
1147.2.a.f	$1147$	$2$	1147.a	1.a	$1$	$9$	$9$	$9.159$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(1\)	\(6\)	\(-9\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1147.2.a.g	$1147$	$2$	1147.a	1.a	$1$	$21$	$21$	$9.159$		None	✓	$1$	$1$	\(-10\)	\(-1\)	\(-15\)	\(-4\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
1147.2.a.h	$1147$	$2$	1147.a	1.a	$1$	$23$	$23$	$9.159$		None	✓	$1$	$0$	\(9\)	\(8\)	\(13\)	\(7\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
1147.2.a.i	$1147$	$2$	1147.a	1.a	$1$	$27$	$27$	$9.159$		None	✓	$1$	$0$	\(9\)	\(1\)	\(11\)	\(6\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1147))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1147)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 2}\)