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

• Label: 896.2.q
• Level: $896$
• Weight: $2$
• Character orbit: 896.q
• Rep. character: $\chi_{896}(703,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $4$
• Sturm bound: $256$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(256\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	288	64	224
Cusp forms	224	64	160
Eisenstein series	64	0	64

Trace form

\( 64 q + 32 q^{9} - 32 q^{25} + 32 q^{49} + 64 q^{57} - 96 q^{73} - 64 q^{81} + 96 q^{89}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
896.2.q.a	$896$	$2$	896.q	56.m	$6$	$16$	$8$	$7.155$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			896.2.q.a	$4$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\beta _{2}-\beta _{3}+\beta _{7})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{5}+\cdots\)
896.2.q.b	$896$	$2$	896.q	56.m	$6$	$16$	$8$	$7.155$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			896.2.q.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 7$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{13}q^{3}+\beta _{7}q^{5}+(-\beta _{10}+\beta _{14}+\cdots)q^{7}+\cdots\)
896.2.q.c	$896$	$2$	896.q	56.m	$6$	$16$	$8$	$7.155$	16.0.\(\cdots\).2	None		✓			896.2.q.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{3}+\beta _{9}q^{5}-\beta _{14}q^{7}+(2\beta _{6}+2\beta _{7}+\cdots)q^{9}+\cdots\)
896.2.q.d	$896$	$2$	896.q	56.m	$6$	$16$	$8$	$7.155$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			896.2.q.a	$4$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\beta _{2}+\beta _{3}-\beta _{7})q^{3}+(\beta _{5}+\beta _{10}+\cdots)q^{5}+\cdots\)

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

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