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

• Label: 1710.2.l
• Level: $1710$
• Weight: $2$
• Character orbit: 1710.l
• Rep. character: $\chi_{1710}(1261,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $72$
• Newform subspaces: $19$
• 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.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	752	72	680
Cusp forms	688	72	616
Eisenstein series	64	0	64

Trace form

\( 72 q - 2 q^{2} - 36 q^{4} + 4 q^{8} + O(q^{10}) \)

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.l.a	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.b	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.c	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
1710.2.l.d	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
1710.2.l.e	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.f	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.g	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.h	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.i	$1710$	$2$	1710.l	19.c	$3$	$2$	$1$	$13.654$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(-1\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
1710.2.l.j	$1710$	$2$	1710.l	19.c	$3$	$4$	$2$	$13.654$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1710.2.l.k	$1710$	$2$	1710.l	19.c	$3$	$4$	$2$	$13.654$	\(\Q(\sqrt{-3}, \sqrt{19})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
1710.2.l.l	$1710$	$2$	1710.l	19.c	$3$	$4$	$2$	$13.654$	\(\Q(\sqrt{-3}, \sqrt{73})\)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{2}q^{4}+(1-\beta _{2})q^{5}+\cdots\)
1710.2.l.m	$1710$	$2$	1710.l	19.c	$3$	$4$	$2$	$13.654$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{4}+\beta _{2}q^{5}+(2+\cdots)q^{7}+\cdots\)
1710.2.l.n	$1710$	$2$	1710.l	19.c	$3$	$4$	$2$	$13.654$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1710.2.l.o	$1710$	$2$	1710.l	19.c	$3$	$6$	$3$	$13.654$	6.0.29654208.1	None		$2$	$0$	\(-3\)	\(0\)	\(-3\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1710.2.l.p	$1710$	$2$	1710.l	19.c	$3$	$6$	$3$	$13.654$	6.0.29654208.1	None		$2$	$0$	\(3\)	\(0\)	\(3\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1710.2.l.q	$1710$	$2$	1710.l	19.c	$3$	$6$	$3$	$13.654$	6.0.29654208.1	None		$2$	$0$	\(3\)	\(0\)	\(3\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1})q^{2}-\beta _{1}q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1710.2.l.r	$1710$	$2$	1710.l	19.c	$3$	$8$	$4$	$13.654$	8.0.4678560000.4	None		$2$	$0$	\(-4\)	\(0\)	\(4\)	\(12\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)
1710.2.l.s	$1710$	$2$	1710.l	19.c	$3$	$8$	$4$	$13.654$	8.0.4678560000.4	None		$2$	$0$	\(4\)	\(0\)	\(-4\)	\(12\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1710, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)