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

• Label: 896.2.e
• Level: $896$
• Weight: $2$
• Character orbit: 896.e
• Rep. character: $\chi_{896}(447,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $256$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(256\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(11\), \(31\)

Dimensions

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

	Total	New	Old
Modular forms	144	32	112
Cusp forms	112	32	80
Eisenstein series	32	0	32

Trace form

\( 32 q - 32 q^{9} + O(q^{10}) \)

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.e.a	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.b	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(-1-\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.c	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-2-\beta _{2})q^{7}+q^{9}+\cdots\)
896.2.e.d	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2+\beta _{2})q^{7}+q^{9}+\cdots\)
896.2.e.e	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.f	$896$	$2$	896.e	56.e	$2$	$4$	$4$	$7.155$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(8\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+(1+\zeta_{12}^{3})q^{5}+\cdots\)
896.2.e.g	$896$	$2$	896.e	56.e	$2$	$8$	$8$	$7.155$	8.0.2517630976.5	\(\Q(\sqrt{-14}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{4}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)