Space of modular forms of level 1280, weight 3, and Character 1280.e

• Label: 1280.3.e
• Level: $1280$
• Weight: $3$
• Character orbit: 1280.e
• Rep. character: $\chi_{1280}(639,\cdot)$
• Character field: $\Q$
• Dimension: $92$
• Newform subspaces: $12$
• Sturm bound: $576$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(576\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1280, [\chi])\).

	Total	New	Old
Modular forms	408	100	308
Cusp forms	360	92	268
Eisenstein series	48	8	40

Trace form

\( 92 q - 244 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1280, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1280.3.e.a	$1280$	$3$	1280.e	40.e	$2$	$2$	$2$	$34.877$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-4+3i)q^{5}+9q^{9}-24q^{13}+2^{4}iq^{17}+\cdots\)
1280.3.e.b	$1280$	$3$	1280.e	40.e	$2$	$2$	$2$	$34.877$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4iq^{3}-5iq^{5}-4q^{7}-7q^{9}+20q^{15}+\cdots\)
1280.3.e.c	$1280$	$3$	1280.e	40.e	$2$	$2$	$2$	$34.877$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4iq^{3}+5iq^{5}+4q^{7}-7q^{9}-20q^{15}+\cdots\)
1280.3.e.d	$1280$	$3$	1280.e	40.e	$2$	$2$	$2$	$34.877$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(4+3i)q^{5}+9q^{9}+24q^{13}-2^{4}iq^{17}+\cdots\)
1280.3.e.e	$1280$	$3$	1280.e	40.e	$2$	$4$	$4$	$34.877$	\(\Q(i, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{3}+5\beta _{1}q^{5}+3\beta _{3}q^{7}-11q^{9}+\cdots\)
1280.3.e.f	$1280$	$3$	1280.e	40.e	$2$	$6$	$6$	$34.877$	6.0.1827904.1	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-2-\beta _{2}+\beta _{5})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1280.3.e.g	$1280$	$3$	1280.e	40.e	$2$	$6$	$6$	$34.877$	6.0.1827904.1	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1+\beta _{4})q^{5}+(2+\beta _{4}+\beta _{5})q^{7}+\cdots\)
1280.3.e.h	$1280$	$3$	1280.e	40.e	$2$	$6$	$6$	$34.877$	6.0.1827904.1	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(-12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1-\beta _{4})q^{5}+(-2-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1280.3.e.i	$1280$	$3$	1280.e	40.e	$2$	$6$	$6$	$34.877$	6.0.1827904.1	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(12\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(2+\beta _{2}-\beta _{5})q^{5}+(2+\beta _{4}+\cdots)q^{7}+\cdots\)
1280.3.e.j	$1280$	$3$	1280.e	40.e	$2$	$8$	$8$	$34.877$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{24}^{2}q^{3}+(-\zeta_{24}-\zeta_{24}^{3})q^{5}-3\zeta_{24}^{4}q^{7}+\cdots\)
1280.3.e.k	$1280$	$3$	1280.e	40.e	$2$	$24$	$24$	$34.877$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
1280.3.e.l	$1280$	$3$	1280.e	40.e	$2$	$24$	$24$	$34.877$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1280, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1280, [\chi]) \cong \)