Space of modular forms of level 1145, weight 2, and trivial character

• Label: 1145.2.a
• Level: $1145$
• Weight: $2$
• Character orbit: 1145.a
• Rep. character: $\chi_{1145}(1,\cdot)$
• Character field: $\Q$
• Dimension: $77$
• Newform subspaces: $6$
• Sturm bound: $230$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1145 = 5 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1145.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(230\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1145))\).

	Total	New	Old
Modular forms	116	77	39
Cusp forms	113	77	36
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.

\(5\)	\(229\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(16\)
\(+\)	\(-\)	$-$	\(22\)
\(-\)	\(+\)	$-$	\(22\)
\(-\)	\(-\)	$+$	\(17\)
Plus space		\(+\)	\(33\)
Minus space		\(-\)	\(44\)

Trace form

\( 77 q - 3 q^{2} + 79 q^{4} + q^{5} - 4 q^{6} + 4 q^{7} - 15 q^{8} + 73 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1145))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	229
1145.2.a.a	$1145$	$2$	1145.a	1.a	$1$	$1$	$1$	$9.143$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(-2\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
1145.2.a.b	$1145$	$2$	1145.a	1.a	$1$	$2$	$2$	$9.143$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(-2\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1+\beta )q^{3}-q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
1145.2.a.c	$1145$	$2$	1145.a	1.a	$1$	$15$	$15$	$9.143$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(4\)	\(0\)	\(-15\)	\(-10\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1145.2.a.d	$1145$	$2$	1145.a	1.a	$1$	$17$	$17$	$9.143$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$1$	\(-8\)	\(-12\)	\(17\)	\(-26\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{12})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1145.2.a.e	$1145$	$2$	1145.a	1.a	$1$	$20$	$20$	$9.143$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(-7\)	\(4\)	\(-20\)	\(20\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
1145.2.a.f	$1145$	$2$	1145.a	1.a	$1$	$22$	$22$	$9.143$		None	✓	$1$	$0$	\(7\)	\(12\)	\(22\)	\(24\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1145))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1145)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(229))\)\(^{\oplus 2}\)