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

• Label: 448.4.e
• Level: $448$
• Weight: $4$
• Character orbit: 448.e
• Rep. character: $\chi_{448}(223,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $4$
• Sturm bound: $256$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	448.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(256\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	204	48	156
Cusp forms	180	48	132
Eisenstein series	24	0	24

Trace form

\( 48 q - 432 q^{9} + O(q^{10}) \)

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.e.a	$448$	$4$	448.e	56.e	$2$	$8$	$8$	$26.433$	8.0.629407744.1	\(\Q(\sqrt{-14}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2\beta _{3}+\beta _{5})q^{3}+(-\beta _{1}-3\beta _{6})q^{5}+\cdots\)
448.4.e.b	$448$	$4$	448.e	56.e	$2$	$8$	$8$	$26.433$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\zeta_{24}^{2}q^{3}-13\zeta_{24}^{6}q^{5}+(7\zeta_{24}+\cdots)q^{7}+\cdots\)
448.4.e.c	$448$	$4$	448.e	56.e	$2$	$8$	$8$	$26.433$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+3\beta _{3}q^{5}+(2\beta _{1}-\beta _{6})q^{7}+\cdots\)
448.4.e.d	$448$	$4$	448.e	56.e	$2$	$24$	$24$	$26.433$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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