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

• Label: 1710.2.c
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.c
• Rep. character: $\chi_{1710}(1709,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $720$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(720\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(7\), \(11\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	376	40	336
Cusp forms	344	40	304
Eisenstein series	32	0	32

Trace form

\( 40 q - 40 q^{4} + 40 q^{16} - 32 q^{19} - 32 q^{25} + 8 q^{49} - 24 q^{55} + 96 q^{61} - 40 q^{64} + 32 q^{76} - 88 q^{85}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1710.2.c.a	$1710$	$2$	1710.c	285.b	$2$	$4$	$4$	$13.654$	\(\Q(\zeta_{8})\)	None		✓			1710.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{8}+\cdots\)
1710.2.c.b	$1710$	$2$	1710.c	285.b	$2$	$4$	$4$	$13.654$	\(\Q(\zeta_{8})\)	None		✓			1710.2.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1710.2.c.c	$1710$	$2$	1710.c	285.b	$2$	$8$	$8$	$13.654$	\(\Q(\zeta_{24})\)	None		✓			1710.2.c.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}-q^{4}+(\beta_{4}+\beta_{3})q^{5}-\beta_1 q^{8}+\cdots\)
1710.2.c.d	$1710$	$2$	1710.c	285.b	$2$	$24$	$24$	$13.654$		None		✓	✓		1710.2.c.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 2}\)