Space of modular forms of level 256, weight 6, and Character 256.b

• Label: 256.6.b
• Level: $256$
• Weight: $6$
• Character orbit: 256.b
• Rep. character: $\chi_{256}(129,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $14$
• Sturm bound: $192$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	256.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(192\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(256, [\chi])\).

	Total	New	Old
Modular forms	172	42	130
Cusp forms	148	38	110
Eisenstein series	24	4	20

Trace form

\( 38 q - 2750 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(256, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
256.6.b.a	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-488\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}+47iq^{5}-244q^{7}+207q^{9}+\cdots\)
256.6.b.b	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-416\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{3}-7iq^{5}-208q^{7}+179q^{9}+\cdots\)
256.6.b.c	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-176\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+6iq^{3}-3^{3}iq^{5}-88q^{7}+99q^{9}+\cdots\)
256.6.b.d	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-48\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+10iq^{3}-37iq^{5}-24q^{7}-157q^{9}+\cdots\)
256.6.b.e	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-41iq^{5}+3^{5}q^{9}+597iq^{13}+2242q^{17}+\cdots\)
256.6.b.f	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(48\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+10iq^{3}+37iq^{5}+24q^{7}-157q^{9}+\cdots\)
256.6.b.g	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(176\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+6iq^{3}+3^{3}iq^{5}+88q^{7}+99q^{9}+\cdots\)
256.6.b.h	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(416\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4iq^{3}+7iq^{5}+208q^{7}+179q^{9}+\cdots\)
256.6.b.i	$256$	$6$	256.b	8.b	$2$	$2$	$2$	$41.058$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(488\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{3}-47iq^{5}+244q^{7}+207q^{9}+\cdots\)
256.6.b.j	$256$	$6$	256.b	8.b	$2$	$4$	$4$	$41.058$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-368\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+(-5^{2}\beta _{1}+2\beta _{2})q^{5}+\cdots\)
256.6.b.k	$256$	$6$	256.b	8.b	$2$	$4$	$4$	$41.058$	\(\Q(i, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-272\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-5\beta _{1}+\beta _{3})q^{3}+(11\beta _{1}-2\beta _{3})q^{5}+\cdots\)
256.6.b.l	$256$	$6$	256.b	8.b	$2$	$4$	$4$	$41.058$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{3}-23\zeta_{12}q^{5}+3\zeta_{12}^{3}q^{7}+\cdots\)
256.6.b.m	$256$	$6$	256.b	8.b	$2$	$4$	$4$	$41.058$	\(\Q(i, \sqrt{19})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(272\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-5\beta _{1}+\beta _{3})q^{3}+(-11\beta _{1}+2\beta _{3})q^{5}+\cdots\)
256.6.b.n	$256$	$6$	256.b	8.b	$2$	$4$	$4$	$41.058$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(368\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}+\beta _{2})q^{3}+(5^{2}\beta _{1}-2\beta _{2})q^{5}+(92+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(256, [\chi]) \cong \)