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

• Label: 1150.3.d
• Level: $1150$
• Weight: $3$
• Character orbit: 1150.d
• Rep. character: $\chi_{1150}(551,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $5$
• Sturm bound: $540$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1150.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(540\)
Trace bound:			\(13\)
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	76	296
Cusp forms	348	76	272
Eisenstein series	24	0	24

Trace form

\( 76 q + 4 q^{3} + 152 q^{4} - 8 q^{6} + 264 q^{9} + O(q^{10}) \)

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.d.a	$1150$	$3$	1150.d	23.b	$2$	$4$	$4$	$31.335$	4.0.613376.1	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(1-\beta _{2})q^{3}+2q^{4}+(2-\beta _{2}+\cdots)q^{6}+\cdots\)
1150.3.d.b	$1150$	$3$	1150.d	23.b	$2$	$16$	$16$	$31.335$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{4}q^{3}+2q^{4}-\beta _{9}q^{6}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1150.3.d.c	$1150$	$3$	1150.d	23.b	$2$	$16$	$16$	$31.335$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+\beta _{5}q^{3}+2q^{4}-\beta _{8}q^{6}+\beta _{1}q^{7}+\cdots\)
1150.3.d.d	$1150$	$3$	1150.d	23.b	$2$	$16$	$16$	$31.335$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{5}q^{3}+2q^{4}-\beta _{8}q^{6}+\beta _{1}q^{7}+\cdots\)
1150.3.d.e	$1150$	$3$	1150.d	23.b	$2$	$24$	$24$	$31.335$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{3}^{\mathrm{old}}(1150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(575, [\chi])\)\(^{\oplus 2}\)