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

• Label: 1710.2.q
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.q
• Rep. character: $\chi_{1710}(179,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $720$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	752	80	672
Cusp forms	688	80	608
Eisenstein series	64	0	64

Trace form

\( 80 q + 40 q^{4} + O(q^{10}) \)

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.q.a	$1710$	$2$	1710.q	285.q	$6$	$16$	$8$	$13.654$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{3}q^{2}+(1-\beta _{1})q^{4}+(-2\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
1710.2.q.b	$1710$	$2$	1710.q	285.q	$6$	$64$	$32$	$13.654$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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