Space of modular forms of level 448, weight 4, and Character 448.t

• Label: 448.4.t
• Level: $448$
• Weight: $4$
• Character orbit: 448.t
• Rep. character: $\chi_{448}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $256$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(256\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(448, [\chi])\).

	Total	New	Old
Modular forms	408	96	312
Cusp forms	360	96	264
Eisenstein series	48	0	48

Trace form

\( 96 q + 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(448, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.4.t.a	$448$	$4$	448.t	56.p	$6$	$32$	$16$	$26.433$		None		$4$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
448.4.t.b	$448$	$4$	448.t	56.p	$6$	$32$	$16$	$26.433$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
448.4.t.c	$448$	$4$	448.t	56.p	$6$	$32$	$16$	$26.433$		None		$4$	$0$	\(0\)	\(0\)	\(24\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)