Space of modular forms of level 1092, weight 2, and Character 1092.c

• Label: 1092.2.c
• Level: $1092$
• Weight: $2$
• Character orbit: 1092.c
• Rep. character: $\chi_{1092}(391,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1092 = 2^{2} \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1092.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1092, [\chi])\).

	Total	New	Old
Modular forms	232	96	136
Cusp forms	216	96	120
Eisenstein series	16	0	16

Trace form

\( 96 q + 4 q^{2} - 4 q^{4} + 28 q^{8} + 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1092, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1092.2.c.a	$1092$	$2$	1092.c	28.d	$2$	$48$	$48$	$8.720$		None		$2$	$0$	\(2\)	\(-48\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1092.2.c.b	$1092$	$2$	1092.c	28.d	$2$	$48$	$48$	$8.720$		None		$2$	$0$	\(2\)	\(48\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1092, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1092, [\chi]) \cong \)