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

• Label: 1280.3.g
• Level: $1280$
• Weight: $3$
• Character orbit: 1280.g
• Rep. character: $\chi_{1280}(1151,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $576$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1280 = 2^{8} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1280.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(576\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	408	64	344
Cusp forms	360	64	296
Eisenstein series	48	0	48

Trace form

\( 64 q + 192 q^{9} + O(q^{10}) \)

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.g.a	$1280$	$3$	1280.g	8.d	$2$	$4$	$4$	$34.877$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-3-\beta _{3})q^{3}-\beta _{2}q^{5}+(\beta _{1}-5\beta _{2}+\cdots)q^{7}+\cdots\)
1280.3.g.b	$1280$	$3$	1280.g	8.d	$2$	$4$	$4$	$34.877$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1280.3.g.c	$1280$	$3$	1280.g	8.d	$2$	$4$	$4$	$34.877$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{3}+\beta _{2}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1280.3.g.d	$1280$	$3$	1280.g	8.d	$2$	$4$	$4$	$34.877$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3+\beta _{3})q^{3}-\beta _{2}q^{5}+(-\beta _{1}+5\beta _{2}+\cdots)q^{7}+\cdots\)
1280.3.g.e	$1280$	$3$	1280.g	8.d	$2$	$8$	$8$	$34.877$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{20}^{4}q^{3}+\zeta_{20}q^{5}+(-\zeta_{20}^{3}-\zeta_{20}^{5}+\cdots)q^{7}+\cdots\)
1280.3.g.f	$1280$	$3$	1280.g	8.d	$2$	$8$	$8$	$34.877$	8.0.12960000.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{4}q^{5}+\beta _{6}q^{7}+(9+3\beta _{1}+\cdots)q^{9}+\cdots\)
1280.3.g.g	$1280$	$3$	1280.g	8.d	$2$	$16$	$16$	$34.877$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)	$2^{36}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{4})q^{3}-\beta _{7}q^{5}+(\beta _{7}+\beta _{9}+\cdots)q^{7}+\cdots\)
1280.3.g.h	$1280$	$3$	1280.g	8.d	$2$	$16$	$16$	$34.877$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)	$2^{36}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{4})q^{3}-\beta _{7}q^{5}+(-\beta _{7}-\beta _{9}+\cdots)q^{7}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1280, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)