Space of modular forms of level 84, weight 4, and Character 84.o

• Label: 84.4.o
• Level: $84$
• Weight: $4$
• Character orbit: 84.o
• Rep. character: $\chi_{84}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $3$

Defining parameters

Level:	$N$	$=$	$84 = 2^{2} \cdot 3 \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	84.o (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$28$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$64$
Trace bound:			$3$
Distinguishing $T_p$:			$11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(84, [\chi])$.

	Total	New	Old
Modular forms	104	48	56
Cusp forms	88	48	40
Eisenstein series	16	0	16

Trace form

48 * q - 2 * q^2 - 10 * q^4 - 152 * q^8 - 216 * q^9 + 18 * q^10 + 142 * q^14 + 86 * q^16 - 18 * q^18 - 120 * q^21 + 28 * q^22 - 270 * q^24 + 684 * q^25 - 750 * q^26 - 578 * q^28 + 800 * q^29 - 168 * q^30 + 108 * q^32 - 36 * q^33 + 180 * q^36 - 268 * q^37 + 1494 * q^38 + 1170 * q^40 - 96 * q^42 + 1468 * q^44 - 108 * q^46 + 536 * q^49 + 2492 * q^50 - 3564 * q^52 - 1144 * q^53 - 3256 * q^56 - 504 * q^57 - 2430 * q^58 + 402 * q^60 - 600 * q^61 - 3292 * q^64 + 280 * q^65 + 2052 * q^66 + 7452 * q^68 + 3778 * q^70 + 684 * q^72 - 972 * q^73 - 10 * q^74 - 1936 * q^77 + 1692 * q^78 - 5976 * q^80 - 1944 * q^81 - 9816 * q^82 - 1320 * q^84 + 3648 * q^85 - 5826 * q^86 + 2566 * q^88 - 952 * q^92 + 468 * q^93 + 9072 * q^94 + 3870 * q^96 + 7896 * q^98

Decomposition of $S_{4}^{\mathrm{new}}(84, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
84.4.o.a	$84$	$4$	84.o	28.f	$6$	$24$	$12$	$4.956$		None		✓			84.4.o.a	$2$	$0$	$-1$	$-36$	$0$	$10$		$\mathrm{SU}(2)[C_{6}]$
84.4.o.b	$84$	$4$	84.o	28.f	$6$	$24$	$12$	$4.956$		None		✓			84.4.o.a	$2$	$0$	$-1$	$36$	$0$	$-10$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{4}^{\mathrm{old}}(84, [\chi])$ into lower level spaces

$S_{4}^{\mathrm{old}}(84, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(28, [\chi])$$^{\oplus 2}$