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

• Label: 448.3.g
• Level: $448$
• Weight: $3$
• Character orbit: 448.g
• Rep. character: $\chi_{448}(351,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
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.g.a	$448$	$3$	448.g	8.d	$2$	$4$	$4$	$12.207$	\(\Q(i, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{2})q^{3}+(-5\beta _{1}+\beta _{3})q^{5}+\cdots\)
448.3.g.b	$448$	$3$	448.g	8.d	$2$	$4$	$4$	$12.207$	\(\Q(i, \sqrt{7})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{2})q^{3}+(5\beta _{1}-\beta _{3})q^{5}+\beta _{3}q^{7}+\cdots\)
448.3.g.c	$448$	$3$	448.g	8.d	$2$	$16$	$16$	$12.207$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{38}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{8}q^{5}-\beta _{10}q^{7}+(5+\beta _{5}+\cdots)q^{9}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)