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

• Label: 256.2.e
• Level: $256$
• Weight: $2$
• Character orbit: 256.e
• Rep. character: $\chi_{256}(65,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(64\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	88	16	72
Cusp forms	40	16	24
Eisenstein series	48	0	48

Trace form

\( 16 q + O(q^{10}) \)

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.e.a	$256$	$2$	256.e	16.e	$4$	$8$	$4$	$2.044$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}^{2}q^{3}-\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
256.2.e.b	$256$	$2$	256.e	16.e	$4$	$8$	$4$	$2.044$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)

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

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