Space of modular forms of level 320, weight 3, and Character 320.b

• Label: 320.3.b
• Level: $320$
• Weight: $3$
• Character orbit: 320.b
• Rep. character: $\chi_{320}(191,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(320, [\chi])\).

	Total	New	Old
Modular forms	108	16	92
Cusp forms	84	16	68
Eisenstein series	24	0	24

Trace form

\( 16 q - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(320, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
320.3.b.a	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots\)
320.3.b.b	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-4\beta _{2})q^{7}+(-5+\cdots)q^{9}+\cdots\)
320.3.b.c	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	\(\Q(\zeta_{10})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{7}+\cdots\)
320.3.b.d	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)