Space of modular forms of level 1145, weight 2, and Character 1145.b

• Label: 1145.2.b
• Level: $1145$
• Weight: $2$
• Character orbit: 1145.b
• Rep. character: $\chi_{1145}(459,\cdot)$
• Character field: $\Q$
• Dimension: $114$
• Newform subspaces: $4$
• Sturm bound: $230$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1145 = 5 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1145.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(230\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1145, [\chi])\).

	Total	New	Old
Modular forms	118	114	4
Cusp forms	114	114	0
Eisenstein series	4	0	4

Trace form

\( 114 q - 114 q^{4} - 4 q^{6} - 118 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1145, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1145.2.b.a	$1145$	$2$	1145.b	5.b	$2$	$4$	$4$	$9.143$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1145.2.b.b	$1145$	$2$	1145.b	5.b	$2$	$4$	$4$	$9.143$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)
1145.2.b.c	$1145$	$2$	1145.b	5.b	$2$	$44$	$44$	$9.143$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1145.2.b.d	$1145$	$2$	1145.b	5.b	$2$	$62$	$62$	$9.143$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$