Space of modular forms of level 448, weight 2, and Character 448.bm

• Label: 448.2.bm
• Level: $448$
• Weight: $2$
• Character orbit: 448.bm
• Rep. character: $\chi_{448}(3,\cdot)$
• Character field: $\Q(\zeta_{48})$
• Dimension: $992$
• Newform subspaces: $1$
• Sturm bound: $128$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.bm (of order \(48\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 448 \)
Character field:			\(\Q(\zeta_{48})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(128\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).

	Total	New	Old
Modular forms	1056	1056	0
Cusp forms	992	992	0
Eisenstein series	64	64	0

Trace form

992 * q - 8 * q^2 - 24 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 24 * q^10 - 8 * q^11 - 24 * q^12 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 24 * q^17 - 8 * q^18 - 24 * q^19 - 16 * q^21 - 48 * q^22 - 8 * q^23 - 24 * q^24 - 8 * q^25 - 24 * q^26 - 56 * q^28 - 32 * q^29 + 72 * q^30 - 48 * q^31 - 8 * q^32 - 16 * q^35 - 192 * q^36 - 8 * q^37 - 24 * q^38 - 8 * q^39 - 24 * q^40 - 56 * q^42 - 32 * q^43 - 24 * q^45 - 8 * q^46 - 24 * q^47 - 16 * q^49 - 80 * q^50 - 8 * q^51 + 120 * q^52 - 8 * q^53 - 24 * q^54 - 16 * q^56 - 32 * q^57 - 8 * q^58 - 216 * q^59 + 88 * q^60 - 24 * q^61 - 224 * q^64 - 16 * q^65 + 264 * q^66 - 88 * q^67 - 24 * q^68 - 16 * q^70 + 96 * q^71 - 8 * q^72 - 24 * q^73 + 48 * q^74 - 24 * q^75 - 16 * q^77 - 128 * q^78 - 8 * q^79 + 48 * q^80 - 8 * q^81 - 264 * q^82 + 96 * q^84 - 32 * q^85 - 8 * q^86 - 24 * q^87 - 8 * q^88 - 24 * q^89 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 24 * q^94 - 16 * q^95 - 432 * q^96 + 120 * q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.2.bm.a	$448$	$2$	448.bm	448.am	$48$	$992$	$62$	$3.577$		None		✓	✓	✓	448.2.bm.a	$4$	$0$	\(-8\)	\(-24\)	\(-24\)	\(-16\)		$\mathrm{SU}(2)[C_{48}]$