Space of modular forms of level 224, weight 4, and Character 224.u

• Label: 224.4.u
• Level: $224$
• Weight: $4$
• Character orbit: 224.u
• Rep. character: $\chi_{224}(29,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $288$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$224 = 2^{5} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	224.u (of order $8$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$32$
Character field:			$\Q(\zeta_{8})$
Newform subspaces:			$2$
Sturm bound:			$128$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(224, [\chi])$.

	Total	New	Old
Modular forms	392	288	104
Cusp forms	376	288	88
Eisenstein series	16	0	16

Trace form

288 * q - 240 * q^10 + 96 * q^12 + 300 * q^16 + 180 * q^18 - 628 * q^22 - 328 * q^23 - 912 * q^24 - 40 * q^26 + 528 * q^27 - 1160 * q^30 - 1240 * q^32 - 1000 * q^34 - 2480 * q^36 - 2408 * q^38 - 1200 * q^39 + 1640 * q^40 - 808 * q^43 + 500 * q^44 + 2880 * q^46 + 4888 * q^48 + 4264 * q^50 + 2976 * q^51 + 1728 * q^52 - 752 * q^53 + 1728 * q^54 + 576 * q^55 - 196 * q^56 - 2376 * q^58 - 8552 * q^60 + 3648 * q^61 - 6840 * q^62 - 2520 * q^63 - 6592 * q^66 - 2040 * q^67 - 5032 * q^68 + 2112 * q^69 - 1008 * q^70 + 3408 * q^72 + 1316 * q^74 + 4416 * q^75 + 10240 * q^76 - 1904 * q^77 + 5064 * q^78 + 15600 * q^80 + 5840 * q^82 + 1848 * q^86 + 2576 * q^87 - 3120 * q^88 - 3720 * q^90 - 13692 * q^92 - 16264 * q^94 + 12160 * q^95 - 12352 * q^96 + 10624 * q^99

Decomposition of $S_{4}^{\mathrm{new}}(224, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
224.4.u.a	$224$	$4$	224.u	32.g	$8$	$140$	$35$	$13.216$		None		✓			224.4.u.a	$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$
224.4.u.b	$224$	$4$	224.u	32.g	$8$	$148$	$37$	$13.216$		None		✓	✓		224.4.u.b	$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{8}]$

Decomposition of $S_{4}^{\mathrm{old}}(224, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(224, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(32, [\chi])$$^{\oplus 2}$