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

• Label: 1280.2.l
• Level: $1280$
• Weight: $2$
• Character orbit: 1280.l
• Rep. character: $\chi_{1280}(321,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(384\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	432	64	368
Cusp forms	336	64	272
Eisenstein series	96	0	96

Trace form

\( 64 q + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.2.l.a	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{24}^{5}+\zeta_{24}^{6})q^{3}-\zeta_{24}q^{5}+(-2\zeta_{24}+\cdots)q^{7}+\cdots\)
1280.2.l.b	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	8.0.349241344.2	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{4})q^{3}-\beta _{2}q^{5}+(-2\beta _{6}-\beta _{7})q^{7}+\cdots\)
1280.2.l.c	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	8.0.349241344.2	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{4})q^{3}+\beta _{2}q^{5}+(2\beta _{6}+\beta _{7})q^{7}+\cdots\)
1280.2.l.d	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{24}^{5}+\zeta_{24}^{6})q^{3}+\zeta_{24}q^{5}+(2\zeta_{24}+\cdots)q^{7}+\cdots\)
1280.2.l.e	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	8.0.349241344.2	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{5}+\beta _{6})q^{3}+\beta _{3}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1280.2.l.f	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{24}-\zeta_{24}^{2}+\zeta_{24}^{3})q^{3}+\zeta_{24}^{5}q^{5}+\cdots\)
1280.2.l.g	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{24}-\zeta_{24}^{2}+\zeta_{24}^{3})q^{3}-\zeta_{24}^{5}q^{5}+\cdots\)
1280.2.l.h	$1280$	$2$	1280.l	16.e	$4$	$8$	$4$	$10.221$	8.0.349241344.2	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{5}+\beta _{6})q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)