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

• Label: 448.4.j
• Level: $448$
• Weight: $4$
• Character orbit: 448.j
• Rep. character: $\chi_{448}(111,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $92$
• Newform subspaces: $2$
• Sturm bound: $256$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(256\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	400	100	300
Cusp forms	368	92	276
Eisenstein series	32	8	24

Trace form

\( 92 q + 4 q^{7} + O(q^{10}) \)

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.j.a	$448$	$4$	448.j	112.j	$4$	$4$	$2$	$26.433$	\(\Q(i, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+7\beta _{2}q^{7}+3^{3}\beta _{1}q^{9}+(34-34\beta _{1}+\cdots)q^{11}+\cdots\)
448.4.j.b	$448$	$4$	448.j	112.j	$4$	$88$	$44$	$26.433$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{4}^{\mathrm{old}}(448, [\chi]) \cong \)