Space of modular forms of level 224, weight 2, and Character 224.u

• Label: 224.2.u
• Level: $224$
• Weight: $2$
• Character orbit: 224.u
• Rep. character: $\chi_{224}(29,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $96$
• Newform subspaces: $3$
• Sturm bound: $64$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(64\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(224, [\chi])\).

	Total	New	Old
Modular forms	136	96	40
Cusp forms	120	96	24
Eisenstein series	16	0	16

Trace form

\( 96 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(224, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.2.u.a	$224$	$2$	224.u	32.g	$8$	$4$	$1$	$1.789$	\(\Q(\zeta_{8})\)	None		$2$	$1$	\(-4\)	\(-4\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
224.2.u.b	$224$	$2$	224.u	32.g	$8$	$40$	$10$	$1.789$		None		$2$	$0$	\(4\)	\(4\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
224.2.u.c	$224$	$2$	224.u	32.g	$8$	$52$	$13$	$1.789$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(224, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(224, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 2}\)