Space of modular forms of level 320, weight 2, and Character 320.q

• Label: 320.2.q
• Level: $320$
• Weight: $2$
• Character orbit: 320.q
• Rep. character: $\chi_{320}(49,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	320.q (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(96\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

	Total	New	Old
Modular forms	112	28	84
Cusp forms	80	20	60
Eisenstein series	32	8	24

Trace form

\( 20 q - 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
320.2.q.a	$320$	$2$	320.q	80.q	$4$	$2$	$1$	$2.555$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-i)q^{3}+(1+2i)q^{5}-iq^{9}+\cdots\)
320.2.q.b	$320$	$2$	320.q	80.q	$4$	$2$	$1$	$2.555$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{3}+(2+i)q^{5}-iq^{9}+(3+3i)q^{11}+\cdots\)
320.2.q.c	$320$	$2$	320.q	80.q	$4$	$16$	$8$	$2.555$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{11}q^{3}+(-1-\beta _{6}-\beta _{10})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

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