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

• Label: 1620.2.d
• Level: $1620$
• Weight: $2$
• Character orbit: 1620.d
• Rep. character: $\chi_{1620}(649,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $648$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(648\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	360	24	336
Cusp forms	288	24	264
Eisenstein series	72	0	72

Trace form

\( 24 q + O(q^{10}) \)

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.d.a	$1620$	$2$	1620.d	5.b	$2$	$2$	$2$	$12.936$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-i)q^{5}+iq^{7}+q^{11}-iq^{17}+\cdots\)
1620.2.d.b	$1620$	$2$	1620.d	5.b	$2$	$2$	$2$	$12.936$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+i)q^{5}+iq^{7}-q^{11}+iq^{17}+\cdots\)
1620.2.d.c	$1620$	$2$	1620.d	5.b	$2$	$6$	$6$	$12.936$	6.0.301925376.2	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}-\beta _{2}q^{11}+\cdots\)
1620.2.d.d	$1620$	$2$	1620.d	5.b	$2$	$6$	$6$	$12.936$	6.0.301925376.2	None		$2$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(\beta _{1}+\beta _{3}-\beta _{4})q^{7}+\beta _{2}q^{11}+\cdots\)
1620.2.d.e	$1620$	$2$	1620.d	5.b	$2$	$8$	$8$	$12.936$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{2}q^{7}+(-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1620, [\chi]) \cong \)