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 - 16 * q^10 - 32 * q^12 - 20 * q^16 - 20 * q^18 - 28 * q^22 - 8 * q^23 - 16 * q^24 + 40 * q^26 - 48 * q^27 + 40 * q^30 + 40 * q^32 + 40 * q^34 + 16 * q^36 - 56 * q^38 - 48 * q^39 + 40 * q^40 - 8 * q^43 + 4 * q^44 - 64 * q^46 - 104 * q^48 - 104 * q^50 + 32 * q^51 - 64 * q^52 - 16 * q^53 + 64 * q^54 + 64 * q^55 + 28 * q^56 + 72 * q^58 - 8 * q^60 - 64 * q^61 + 24 * q^62 + 40 * q^63 - 64 * q^66 + 40 * q^67 - 8 * q^68 - 64 * q^69 + 48 * q^70 - 48 * q^72 + 28 * q^74 + 64 * q^75 - 16 * q^77 + 24 * q^78 - 16 * q^80 - 80 * q^82 + 40 * q^86 - 112 * q^87 + 80 * q^88 - 120 * q^90 + 148 * q^92 + 40 * q^94 - 128 * q^95 - 64 * q^96 - 128 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.2.u.a	$224$	$2$	224.u	32.g	$8$	$4$	$1$	$1.789$	\(\Q(\zeta_{8})\)	None		✓			224.2.u.a	$2$	$1$	\(-4\)	\(-4\)	\(-8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-1+\zeta_{8}^{2})q^{2}+(-1-\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
224.2.u.b	$224$	$2$	224.u	32.g	$8$	$40$	$10$	$1.789$		None		✓			224.2.u.b	$2$	$0$	\(4\)	\(4\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
224.2.u.c	$224$	$2$	224.u	32.g	$8$	$52$	$13$	$1.789$		None		✓	✓		224.2.u.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

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

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