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

• Label: 448.3.h
• Level: $448$
• Weight: $3$
• Character orbit: 448.h
• Rep. character: $\chi_{448}(97,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	448.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
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	32	108
Cusp forms	116	32	84
Eisenstein series	24	0	24

Trace form

\( 32 q + 96 q^{9} + 160 q^{25} - 32 q^{49} + 192 q^{57} + 480 q^{81}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
448.3.h.a	$448$	$3$	448.h	56.h	$2$	$8$	$8$	$12.207$	8.0.\(\cdots\).2	None		✓			448.3.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{3}q^{5}-\beta _{4}q^{7}+q^{9}-\beta _{2}q^{11}+\cdots\)
448.3.h.b	$448$	$3$	448.h	56.h	$2$	$24$	$24$	$12.207$		None		✓	✓		448.3.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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