Space of modular forms of level 1150, weight 3, and Character 1150.c

• Label: 1150.3.c
• Level: $1150$
• Weight: $3$
• Character orbit: 1150.c
• Rep. character: $\chi_{1150}(1149,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $540$
• Trace bound: $26$

Defining parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(540\)
Trace bound:			\(26\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1150, [\chi])\).

	Total	New	Old
Modular forms	372	72	300
Cusp forms	348	72	276
Eisenstein series	24	0	24

Trace form

\( 72 q - 144 q^{4} - 16 q^{6} - 208 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1150, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1150.3.c.a	$1150$	$3$	1150.c	115.c	$2$	$8$	$8$	$31.335$	8.0.\(\cdots\).5	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4})q^{3}-2q^{4}+(2+\cdots)q^{6}+\cdots\)
1150.3.c.b	$1150$	$3$	1150.c	115.c	$2$	$32$	$32$	$31.335$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1150.3.c.c	$1150$	$3$	1150.c	115.c	$2$	$32$	$32$	$31.335$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1150, [\chi]) \cong \)