Space of modular forms of level 1620, weight 3, and Character 1620.t

• Label: 1620.3.t
• Level: $1620$
• Weight: $3$
• Character orbit: 1620.t
• Rep. character: $\chi_{1620}(269,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $972$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1620.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(972\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1620, [\chi])\).

	Total	New	Old
Modular forms	1368	96	1272
Cusp forms	1224	96	1128
Eisenstein series	144	0	144

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1620, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1620.3.t.a	$1620$	$3$	1620.t	45.h	$6$	$8$	$4$	$44.142$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}-\beta _{7})q^{5}+\beta _{1}q^{7}+(-3\beta _{1}-2\beta _{4}+\cdots)q^{11}+\cdots\)
1620.3.t.b	$1620$	$3$	1620.t	45.h	$6$	$8$	$4$	$44.142$	8.0.12960000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{5}-2\beta _{4}q^{7}+(\beta _{2}+2\beta _{5}+2\beta _{6}+\cdots)q^{11}+\cdots\)
1620.3.t.c	$1620$	$3$	1620.t	45.h	$6$	$8$	$4$	$44.142$	8.0.\(\cdots\).6	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{2}+\beta _{5}+\beta _{6})q^{5}+\beta _{3}q^{7}-7\beta _{4}q^{11}+\cdots\)
1620.3.t.d	$1620$	$3$	1620.t	45.h	$6$	$8$	$4$	$44.142$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}+\beta _{7})q^{5}+\beta _{1}q^{7}+(3\beta _{1}+2\beta _{4}+\cdots)q^{11}+\cdots\)
1620.3.t.e	$1620$	$3$	1620.t	45.h	$6$	$16$	$8$	$44.142$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{4}q^{5}+(-\beta _{3}+\beta _{7})q^{7}+\beta _{14}q^{11}+\cdots\)
1620.3.t.f	$1620$	$3$	1620.t	45.h	$6$	$48$	$24$	$44.142$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1620, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1620, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(405, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(810, [\chi])\)\(^{\oplus 2}\)