Space of modular forms of level 1692, weight 2, and Character 1692.j

• Label: 1692.2.j
• Level: $1692$
• Weight: $2$
• Character orbit: 1692.j
• Rep. character: $\chi_{1692}(281,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1692 = 2^{2} \cdot 3^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1692.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 423 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1692, [\chi])\).

	Total	New	Old
Modular forms	588	96	492
Cusp forms	564	96	468
Eisenstein series	24	0	24

Trace form

\( 96 q + 2 q^{3} - 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1692, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1692.2.j.a	$1692$	$2$	1692.j	423.g	$6$	$96$	$48$	$13.511$		None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1692, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1692, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(423, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(846, [\chi])\)\(^{\oplus 2}\)