Space of modular forms of level 1710, weight 2, and Character 1710.bq

• Label: 1710.2.bq
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.bq
• Rep. character: $\chi_{1710}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $720$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.bq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(720\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1710, [\chi])\).

	Total	New	Old
Modular forms	752	64	688
Cusp forms	688	64	624
Eisenstein series	64	0	64

Trace form

\( 64 q - 32 q^{4} + 16 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1710, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1710.2.bq.a	$1710$	$2$	1710.bq	57.f	$6$	$32$	$16$	$13.654$		None		$2$	$0$	\(-16\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{6}]$
1710.2.bq.b	$1710$	$2$	1710.bq	57.f	$6$	$32$	$16$	$13.654$		None		$2$	$0$	\(16\)	\(0\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1710, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \)