Space of modular forms of level 448, weight 3, and Character 448.d

• Label: 448.3.d
• Level: $448$
• Weight: $3$
• Character orbit: 448.d
• Rep. character: $\chi_{448}(127,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(448, [\chi])\).

	Total	New	Old
Modular forms	140	24	116
Cusp forms	116	24	92
Eisenstein series	24	0	24

Trace form

\( 24 q - 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(448, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.3.d.a	$448$	$3$	448.d	4.b	$2$	$2$	$2$	$12.207$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{3}-8q^{5}-\beta q^{7}-19q^{9}-4\beta q^{11}+\cdots\)
448.3.d.b	$448$	$3$	448.d	4.b	$2$	$4$	$4$	$12.207$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{3})q^{3}+(1-\beta _{1})q^{5}-\beta _{3}q^{7}+\cdots\)
448.3.d.c	$448$	$3$	448.d	4.b	$2$	$4$	$4$	$12.207$	\(\Q(i, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}+\beta _{3}q^{7}+5q^{9}+\cdots\)
448.3.d.d	$448$	$3$	448.d	4.b	$2$	$6$	$6$	$12.207$	6.0.1539727.2	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(1-\beta _{2})q^{5}+\beta _{1}q^{7}+(-2+\cdots)q^{9}+\cdots\)
448.3.d.e	$448$	$3$	448.d	4.b	$2$	$8$	$8$	$12.207$	8.0.1997017344.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{3}q^{7}+(-5+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)