Space of modular forms of level 1122, weight 3, and Character 1122.d

• Label: 1122.3.d
• Level: $1122$
• Weight: $3$
• Character orbit: 1122.d
• Rep. character: $\chi_{1122}(373,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $648$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1122.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 187 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(648\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1122, [\chi])\).

	Total	New	Old
Modular forms	440	72	368
Cusp forms	424	72	352
Eisenstein series	16	0	16

Trace form

\( 72 q - 144 q^{4} - 216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1122, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1122.3.d.a	$1122$	$3$	1122.d	187.b	$2$	$72$	$72$	$30.572$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1122, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1122, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(374, [\chi])\)\(^{\oplus 2}\)