Space of modular forms of level 1280, weight 2, and Character 1280.q

• Label: 1280.2.q
• Level: $1280$
• Weight: $2$
• Character orbit: 1280.q
• Rep. character: $\chi_{1280}(449,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.q (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1280, [\chi])\).

	Total	New	Old
Modular forms	432	96	336
Cusp forms	336	96	240
Eisenstein series	96	0	96

Trace form

\( 96 q + 96 q^{49} + 96 q^{65} - 96 q^{81}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1280, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.2.q.a	$1280$	$2$	1280.q	80.q	$4$	$16$	$8$	$10.221$	16.0.\(\cdots\).9	None		✓			1280.2.q.a	$8$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{3}+(-\beta _{4}+\beta _{9}-\beta _{15})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1280.2.q.b	$1280$	$2$	1280.q	80.q	$4$	$16$	$8$	$10.221$	16.0.\(\cdots\).9	None		✓			1280.2.q.a	$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{3}+(\beta _{4}-\beta _{9}+\beta _{15})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1280.2.q.c	$1280$	$2$	1280.q	80.q	$4$	$32$	$16$	$10.221$		None		✓			1280.2.q.c	$8$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
1280.2.q.d	$1280$	$2$	1280.q	80.q	$4$	$32$	$16$	$10.221$		None		✓			1280.2.q.c	$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)