Space of modular forms of level 256, weight 2, and Character 256.b

• Label: 256.2.b
• Level: $256$
• Weight: $2$
• Character orbit: 256.b
• Rep. character: $\chi_{256}(129,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $64$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(256, [\chi])\).

	Total	New	Old
Modular forms	44	10	34
Cusp forms	20	6	14
Eisenstein series	24	4	20

Trace form

\( 6 q + 2 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(256, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
256.2.b.a	$256$	$2$	256.b	8.b	$2$	$2$	$2$	$2.044$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+iq^{11}+\cdots\)
256.2.b.b	$256$	$2$	256.b	8.b	$2$	$2$	$2$	$2.044$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+iq^{5}+3q^{9}+3iq^{13}+2q^{17}+q^{25}+\cdots\)
256.2.b.c	$256$	$2$	256.b	8.b	$2$	$2$	$2$	$2.044$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+iq^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

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