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

• Label: 1280.2.c
• Level: $1280$
• Weight: $2$
• Character orbit: 1280.c
• Rep. character: $\chi_{1280}(769,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $13$
• Sturm bound: $384$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1280.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(384\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(29\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	216	52	164
Cusp forms	168	44	124
Eisenstein series	48	8	40

Trace form

\( 44 q - 28 q^{9} + O(q^{10}) \)

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.c.a	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2+i)q^{5}+3q^{9}-6iq^{13}+8iq^{17}+\cdots\)
1280.2.c.b	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-2\beta q^{7}+3q^{9}-2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.c	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}+2\beta q^{7}+3q^{9}+2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.d	$1280$	$2$	1280.c	5.b	$2$	$2$	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(2+i)q^{5}+3q^{9}-6iq^{13}-8iq^{17}+\cdots\)
1280.2.c.e	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}-3q^{9}+\cdots\)
1280.2.c.f	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+3\beta _{1}q^{7}-7q^{9}+\cdots\)
1280.2.c.g	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1280.2.c.h	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-3q^{9}+\cdots\)
1280.2.c.i	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
1280.2.c.j	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+q^{9}+\beta _{2}q^{15}+\cdots\)
1280.2.c.k	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots\)
1280.2.c.l	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{5}-\beta _{1}q^{7}+3q^{9}-\beta _{3}q^{11}+\cdots\)
1280.2.c.m	$1280$	$2$	1280.c	5.b	$2$	$4$	$4$	$10.221$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}-3q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)