Space of modular forms of level 256, weight 3, and Character 256.c

• Label: 256.3.c
• Level: $256$
• Weight: $3$
• Character orbit: 256.c
• Rep. character: $\chi_{256}(255,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $7$
• Sturm bound: $96$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(96\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(256, [\chi])\).

	Total	New	Old
Modular forms	76	18	58
Cusp forms	52	14	38
Eisenstein series	24	4	20

Trace form

\( 14 q - 26 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(256, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
256.3.c.a	$256$	$3$	256.c	4.b	$2$	$1$	$1$	$6.975$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8q^{5}+9q^{9}+24q^{13}+30q^{17}+\cdots\)
256.3.c.b	$256$	$3$	256.c	4.b	$2$	$1$	$1$	$6.975$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+8q^{5}+9q^{9}-24q^{13}+30q^{17}+\cdots\)
256.3.c.c	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-4q^{5}+4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots\)
256.3.c.d	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{3}-23q^{9}+3\beta q^{11}-2q^{17}+\cdots\)
256.3.c.e	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{3}+5q^{9}+7iq^{11}+2q^{17}+17iq^{19}+\cdots\)
256.3.c.f	$256$	$3$	256.c	4.b	$2$	$2$	$2$	$6.975$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+4q^{5}-4\beta q^{7}+q^{9}-5\beta q^{11}+\cdots\)
256.3.c.g	$256$	$3$	256.c	4.b	$2$	$4$	$4$	$6.975$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)