Space of modular forms of level 1680, weight 3, and Character 1680.bd

• Label: 1680.3.bd
• Level: $1680$
• Weight: $3$
• Character orbit: 1680.bd
• Rep. character: $\chi_{1680}(769,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bd (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1680, [\chi])\).

	Total	New	Old
Modular forms	792	96	696
Cusp forms	744	96	648
Eisenstein series	48	0	48

Trace form

\( 96 q + 288 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1680, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1680.3.bd.a	$1680$	$3$	1680.bd	35.c	$2$	$16$	$16$	$45.777$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{9}+\cdots)q^{7}+\cdots\)
1680.3.bd.b	$1680$	$3$	1680.bd	35.c	$2$	$16$	$16$	$45.777$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+(\beta _{6}+\beta _{11})q^{5}-\beta _{10}q^{7}+\cdots\)
1680.3.bd.c	$1680$	$3$	1680.bd	35.c	$2$	$16$	$16$	$45.777$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{8}-\beta _{12})q^{5}+\beta _{10}q^{7}+\cdots\)
1680.3.bd.d	$1680$	$3$	1680.bd	35.c	$2$	$48$	$48$	$45.777$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1680, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1680, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 2}\)