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

• Label: 320.3.m
• Level: $320$
• Weight: $3$
• Character orbit: 320.m
• Rep. character: $\chi_{320}(33,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $144$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(144\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	216	48	168
Cusp forms	168	48	120
Eisenstein series	48	0	48

Trace form

\( 48 q + O(q^{10}) \)

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.m.a	$320$	$3$	320.m	40.i	$4$	$8$	$4$	$8.719$	8.0.\(\cdots\).4	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{1}-\beta _{4})q^{3}+\beta _{3}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
320.3.m.b	$320$	$3$	320.m	40.i	$4$	$8$	$4$	$8.719$	8.0.\(\cdots\).4	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{4}q^{5}+(\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
320.3.m.c	$320$	$3$	320.m	40.i	$4$	$16$	$8$	$8.719$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{3}+\beta _{10}q^{5}+(\beta _{1}+\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots\)
320.3.m.d	$320$	$3$	320.m	40.i	$4$	$16$	$8$	$8.719$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{3}q^{3}-\beta _{10}q^{5}+(\beta _{1}+\beta _{5}+\beta _{7}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)