Space of modular forms of level 256, weight 12, and Character 256.b

• Label: 256.12.b
• Level: $256$
• Weight: $12$
• Character orbit: 256.b
• Rep. character: $\chi_{256}(129,\cdot)$
• Character field: $\Q$
• Dimension: $86$
• Newform subspaces: $17$
• Sturm bound: $384$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	256.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(384\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(256, [\chi])\).

	Total	New	Old
Modular forms	364	90	274
Cusp forms	340	86	254
Eisenstein series	24	4	20

Trace form

\( 86 q - 4842014 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(256, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
256.12.b.a	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-110928\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+18iq^{3}+1745iq^{5}-55464q^{7}+\cdots\)
256.12.b.b	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-98608\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+258iq^{3}-5265iq^{5}-49304q^{7}+\cdots\)
256.12.b.c	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-33488\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+126iq^{3}+2415iq^{5}-16744q^{7}+\cdots\)
256.12.b.d	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+6469iq^{5}+3^{11}q^{9}+1315911iq^{13}+\cdots\)
256.12.b.e	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(33488\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+126iq^{3}-2415iq^{5}+16744q^{7}+\cdots\)
256.12.b.f	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(98608\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+258iq^{3}+5265iq^{5}+49304q^{7}+\cdots\)
256.12.b.g	$256$	$12$	256.b	8.b	$2$	$2$	$2$	$196.696$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(110928\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+18iq^{3}-1745iq^{5}+55464q^{7}+\cdots\)
256.12.b.h	$256$	$12$	256.b	8.b	$2$	$4$	$4$	$196.696$	\(\Q(i, \sqrt{109})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-182112\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-14\beta _{1}+\beta _{2})q^{3}+(1967\beta _{1}+12\beta _{2}+\cdots)q^{5}+\cdots\)
256.12.b.i	$256$	$12$	256.b	8.b	$2$	$4$	$4$	$196.696$	\(\Q(i, \sqrt{273})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}-3515\beta _{1}q^{5}+33\beta _{3}q^{7}+\cdots\)
256.12.b.j	$256$	$12$	256.b	8.b	$2$	$4$	$4$	$196.696$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 3^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}+5\zeta_{12}q^{5}-31\zeta_{12}^{3}q^{7}+\cdots\)
256.12.b.k	$256$	$12$	256.b	8.b	$2$	$4$	$4$	$196.696$	\(\Q(i, \sqrt{109})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(182112\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-14\beta _{1}+\beta _{2})q^{3}+(-1967\beta _{1}-12\beta _{2}+\cdots)q^{5}+\cdots\)
256.12.b.l	$256$	$12$	256.b	8.b	$2$	$6$	$6$	$196.696$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-12064\)	$2^{34}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-18\beta _{1}-\beta _{3})q^{3}+(-2^{5}\beta _{1}-\beta _{5})q^{5}+\cdots\)
256.12.b.m	$256$	$12$	256.b	8.b	$2$	$6$	$6$	$196.696$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12064\)	$2^{34}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-18\beta _{1}-\beta _{3})q^{3}+(2^{5}\beta _{1}+\beta _{5})q^{5}+\cdots\)
256.12.b.n	$256$	$12$	256.b	8.b	$2$	$10$	$10$	$196.696$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-35720\)	$2^{74}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{1}-\beta _{4})q^{3}+(-3^{3}\beta _{1}+5\beta _{4}-\beta _{7}+\cdots)q^{5}+\cdots\)
256.12.b.o	$256$	$12$	256.b	8.b	$2$	$10$	$10$	$196.696$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(35720\)	$2^{74}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(3\beta _{1}-\beta _{4})q^{3}+(3^{3}\beta _{1}-5\beta _{4}+\beta _{7}+\cdots)q^{5}+\cdots\)
256.12.b.p	$256$	$12$	256.b	8.b	$2$	$12$	$12$	$196.696$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-98736\)	$2^{110}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-9\beta _{1}+4\beta _{2}+\beta _{6})q^{5}+\cdots\)
256.12.b.q	$256$	$12$	256.b	8.b	$2$	$12$	$12$	$196.696$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(98736\)	$2^{110}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(9\beta _{1}-4\beta _{2}-\beta _{6})q^{5}+(8228+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(256, [\chi]) \cong \)