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

• Label: 896.2.bi
• Level: $896$
• Weight: $2$
• Character orbit: 896.bi
• Rep. character: $\chi_{896}(47,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $256$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bi (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 224 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(256\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	1088	272	816
Cusp forms	960	240	720
Eisenstein series	128	32	96

Trace form

240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 + 32 * q^15 + 12 * q^19 - 8 * q^21 - 4 * q^23 - 4 * q^25 - 16 * q^29 - 24 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 + 32 * q^43 - 48 * q^45 + 24 * q^47 - 20 * q^51 - 20 * q^53 - 16 * q^57 - 84 * q^59 - 12 * q^61 - 8 * q^65 - 36 * q^67 + 80 * q^71 - 12 * q^73 + 72 * q^75 - 8 * q^77 + 8 * q^79 + 24 * q^85 + 12 * q^87 - 12 * q^89 - 40 * q^91 + 20 * q^93 + 40 * q^99

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.bi.a	$896$	$2$	896.bi	224.ae	$24$	$240$	$30$	$7.155$		None			✓	✓	224.2.be.a	$4$	$0$	\(0\)	\(12\)	\(-12\)	\(8\)		$\mathrm{SU}(2)[C_{24}]$

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

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