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

• Label: 448.2.bd
• Level: $448$
• Weight: $2$
• Character orbit: 448.bd
• Rep. character: $\chi_{448}(27,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $496$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.bd (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 448 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	528	528	0
Cusp forms	496	496	0
Eisenstein series	32	32	0

Trace form

\( 496 q - 16 q^{2} - 16 q^{4} - 8 q^{7} - 16 q^{8} - 16 q^{9} + O(q^{10}) \)

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.bd.a	$448$	$2$	448.bd	448.ad	$16$	$16$	$2$	$3.577$	16.0.\(\cdots\).1	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{16}]$	\(q+\beta _{11}q^{2}+(-\beta _{8}+\beta _{14})q^{4}+(\beta _{5}-2\beta _{7}+\cdots)q^{7}+\cdots\)
448.2.bd.b	$448$	$2$	448.bd	448.ad	$16$	$480$	$60$	$3.577$		None		$4$	$0$	\(-16\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$