Space of modular forms of level 1136, weight 3, and Character 1136.h

• Label: 1136.3.h
• Level: $1136$
• Weight: $3$
• Character orbit: 1136.h
• Rep. character: $\chi_{1136}(993,\cdot)$
• Character field: $\Q$
• Dimension: $71$
• Newform subspaces: $5$
• Sturm bound: $432$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1136 = 2^{4} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1136.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 71 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(432\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1136, [\chi])\).

	Total	New	Old
Modular forms	294	73	221
Cusp forms	282	71	211
Eisenstein series	12	2	10

Trace form

\( 71 q + 2 q^{3} - 2 q^{5} + 205 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1136, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1136.3.h.a	$1136$	$3$	1136.h	71.b	$2$	$4$	$4$	$30.954$	4.0.2836736.1	None		$2$	$0$	\(0\)	\(4\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{3}+(-2+\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots\)
1136.3.h.b	$1136$	$3$	1136.h	71.b	$2$	$7$	$7$	$30.954$	7.7.\(\cdots\).1	\(\Q(\sqrt{-71}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{5}q^{3}-\beta _{3}q^{5}+(9-\beta _{2}-\beta _{4})q^{9}+\cdots\)
1136.3.h.c	$1136$	$3$	1136.h	71.b	$2$	$12$	$12$	$30.954$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-4\)	\(12\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{8}q^{3}+(1-\beta _{6})q^{5}+\beta _{7}q^{7}+(1+2\beta _{2}+\cdots)q^{9}+\cdots\)
1136.3.h.d	$1136$	$3$	1136.h	71.b	$2$	$12$	$12$	$30.954$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(2\)	\(-6\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{5})q^{5}+\beta _{9}q^{7}+(4+\cdots)q^{9}+\cdots\)
1136.3.h.e	$1136$	$3$	1136.h	71.b	$2$	$36$	$36$	$30.954$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1136, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1136, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(71, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(142, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(284, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(568, [\chi])\)\(^{\oplus 2}\)