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

• Label: 896.2.m
• Level: $896$
• Weight: $2$
• Character orbit: 896.m
• Rep. character: $\chi_{896}(225,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $256$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(256\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	288	48	240
Cusp forms	224	48	176
Eisenstein series	64	0	64

Trace form

\( 48 q + O(q^{10}) \)

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.m.a	$896$	$2$	896.m	16.e	$4$	$2$	$1$	$7.155$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(-4\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2+2i)q^{3}+(2+2i)q^{5}-iq^{7}+\cdots\)
896.2.m.b	$896$	$2$	896.m	16.e	$4$	$2$	$1$	$7.155$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2i)q^{5}-iq^{7}+3iq^{9}+(-1+\cdots)q^{11}+\cdots\)
896.2.m.c	$896$	$2$	896.m	16.e	$4$	$2$	$1$	$7.155$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2i)q^{5}+iq^{7}+3iq^{9}+(1+\cdots)q^{11}+\cdots\)
896.2.m.d	$896$	$2$	896.m	16.e	$4$	$2$	$1$	$7.155$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(4\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2-2i)q^{3}+(2+2i)q^{5}+iq^{7}-5iq^{9}+\cdots\)
896.2.m.e	$896$	$2$	896.m	16.e	$4$	$8$	$4$	$7.155$	8.0.214798336.3	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}-\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots\)
896.2.m.f	$896$	$2$	896.m	16.e	$4$	$8$	$4$	$7.155$	8.0.214798336.3	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{4}q^{3}-\beta _{1}q^{5}+\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots\)
896.2.m.g	$896$	$2$	896.m	16.e	$4$	$12$	$6$	$7.155$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+\cdots\)
896.2.m.h	$896$	$2$	896.m	16.e	$4$	$12$	$6$	$7.155$	12.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(4\)	\(-4\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{3}-\beta _{5})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(896, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)