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

• Label: 448.2.bn
• Level: $448$
• Weight: $2$
• Character orbit: 448.bn
• Rep. character: $\chi_{448}(37,\cdot)$
• 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.bn (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

\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.2.bn.a	$448$	$2$	448.bn	448.an	$48$	$992$	$62$	$3.577$		None		$4$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-16\)		$\mathrm{SU}(2)[C_{48}]$