Space of modular forms of level 1680, weight 2, and Character 1680.v

• Label: 1680.2.v
• Level: $1680$
• Weight: $2$
• Character orbit: 1680.v
• Rep. character: $\chi_{1680}(239,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $4$
• Sturm bound: $768$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.v (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 60 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(768\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(11\), \(43\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1680, [\chi])\).

	Total	New	Old
Modular forms	408	72	336
Cusp forms	360	72	288
Eisenstein series	48	0	48

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1680, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1680.2.v.a	$1680$	$2$	1680.v	60.h	$2$	$12$	$12$	$13.415$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(-12\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{5}+\cdots\)
1680.2.v.b	$1680$	$2$	1680.v	60.h	$2$	$12$	$12$	$13.415$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(12\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(\beta _{1}-\beta _{2}-\beta _{3}-\beta _{4})q^{5}+\cdots\)
1680.2.v.c	$1680$	$2$	1680.v	60.h	$2$	$24$	$24$	$13.415$		None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(24\)		$\mathrm{SU}(2)[C_{2}]$
1680.2.v.d	$1680$	$2$	1680.v	60.h	$2$	$24$	$24$	$13.415$		None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)