Space of modular forms of level 1620, weight 2, and Character 1620.i

• Label: 1620.2.i
• Level: $1620$
• Weight: $2$
• Character orbit: 1620.i
• Rep. character: $\chi_{1620}(541,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $14$
• Sturm bound: $648$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(648\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1620, [\chi])\).

	Total	New	Old
Modular forms	720	32	688
Cusp forms	576	32	544
Eisenstein series	144	0	144

Trace form

\( 32 q + 10 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1620, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1620.2.i.a	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.b	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.c	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1620.2.i.d	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1620.2.i.e	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.f	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.g	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+(-3+3\zeta_{6})q^{11}+\cdots\)
1620.2.i.h	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.i	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}-2\zeta_{6}q^{13}+\cdots\)
1620.2.i.j	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
1620.2.i.k	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(-6+6\zeta_{6})q^{11}+\cdots\)
1620.2.i.l	$1620$	$2$	1620.i	9.c	$3$	$2$	$1$	$12.936$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+(3-3\zeta_{6})q^{11}+\cdots\)
1620.2.i.m	$1620$	$2$	1620.i	9.c	$3$	$4$	$2$	$12.936$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\cdots\)
1620.2.i.n	$1620$	$2$	1620.i	9.c	$3$	$4$	$2$	$12.936$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(2\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{12})q^{5}+(\zeta_{12}-\zeta_{12}^{2})q^{7}+\zeta_{12}^{2}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(324, [\chi])\)\(^{\oplus 2}\)