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

• Label: 1710.2.d
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.d
• Rep. character: $\chi_{1710}(1369,\cdot)$
• Character field: $\Q$
• Dimension: $46$
• Newform subspaces: $8$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	376	46	330
Cusp forms	344	46	298
Eisenstein series	32	0	32

Trace form

\( 46 q - 46 q^{4} - 6 q^{5} + O(q^{10}) \)

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.d.a	$1710$	$2$	1710.d	5.b	$2$	$2$	$2$	$13.654$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{4}+(-2+i)q^{5}-iq^{8}+\cdots\)
1710.2.d.b	$1710$	$2$	1710.d	5.b	$2$	$2$	$2$	$13.654$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}-q^{4}+(1+2i)q^{5}+iq^{8}+(2+\cdots)q^{10}+\cdots\)
1710.2.d.c	$1710$	$2$	1710.d	5.b	$2$	$4$	$4$	$13.654$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
1710.2.d.d	$1710$	$2$	1710.d	5.b	$2$	$6$	$6$	$13.654$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1710.2.d.e	$1710$	$2$	1710.d	5.b	$2$	$6$	$6$	$13.654$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1710.2.d.f	$1710$	$2$	1710.d	5.b	$2$	$6$	$6$	$13.654$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
1710.2.d.g	$1710$	$2$	1710.d	5.b	$2$	$8$	$8$	$13.654$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}q^{2}-q^{4}+\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
1710.2.d.h	$1710$	$2$	1710.d	5.b	$2$	$12$	$12$	$13.654$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-q^{4}-\beta _{2}q^{5}-\beta _{1}q^{7}+\beta _{3}q^{8}+\cdots\)

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

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