Space of modular forms of level 896, weight 2, and Character 896.z

• Label: 896.2.z
• Level: $896$
• Weight: $2$
• Character orbit: 896.z
• Rep. character: $\chi_{896}(31,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $112$
• Newform subspaces: $2$
• Sturm bound: $256$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.z (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(256\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(896, [\chi])\).

	Total	New	Old
Modular forms	576	144	432
Cusp forms	448	112	336
Eisenstein series	128	32	96

Trace form

\( 112 q + 12 q^{5} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(896, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
896.2.z.a	$896$	$2$	896.z	112.v	$12$	$56$	$14$	$7.155$		None		$4$	$0$	\(0\)	\(-6\)	\(6\)	\(8\)		$\mathrm{SU}(2)[C_{12}]$
896.2.z.b	$896$	$2$	896.z	112.v	$12$	$56$	$14$	$7.155$		None		$4$	$0$	\(0\)	\(6\)	\(6\)	\(-8\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(896, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)