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

• Label: 84.4.i
• Level: $84$
• Weight: $4$
• Character orbit: 84.i
• Rep. character: $\chi_{84}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $8$
• 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.i (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$7$
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$2$
Sturm bound:			$64$
Trace bound:			$3$
Distinguishing $T_p$:			$5$

Dimensions

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

	Total	New	Old
Modular forms	108	8	100
Cusp forms	84	8	76
Eisenstein series	24	0	24

Trace form

8 * q - 8 * q^5 - 14 * q^7 - 36 * q^9 + 56 * q^11 + 132 * q^13 + 84 * q^15 - 124 * q^17 - 236 * q^19 - 12 * q^21 + 116 * q^23 + 82 * q^25 + 472 * q^29 - 270 * q^31 - 138 * q^33 - 760 * q^35 + 178 * q^37 + 168 * q^39 + 24 * q^41 + 448 * q^43 - 72 * q^45 + 36 * q^47 + 44 * q^49 - 228 * q^51 - 780 * q^53 - 740 * q^55 - 612 * q^57 + 1096 * q^59 + 204 * q^61 + 252 * q^63 + 864 * q^65 + 764 * q^67 + 1608 * q^69 + 392 * q^71 + 146 * q^73 + 312 * q^75 + 244 * q^77 - 1278 * q^79 - 324 * q^81 - 3616 * q^83 - 3848 * q^85 - 942 * q^87 + 1152 * q^89 + 3900 * q^91 - 1362 * q^93 - 148 * q^95 + 2804 * q^97 - 1008 * q^99

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.i.a	$84$	$4$	84.i	7.c	$3$	$4$	$2$	$4.956$	$\Q(\sqrt{-3}, \sqrt{193})$	None		✓			84.4.i.a	$2$	$0$	$0$	$-6$	$-11$	$6$	$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-3+3\beta _{2})q^{3}+(\beta _{1}-6\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots$
84.4.i.b	$84$	$4$	84.i	7.c	$3$	$4$	$2$	$4.956$	$\Q(\sqrt{-3}, \sqrt{-19})$	None		✓			84.4.i.b	$2$	$0$	$0$	$6$	$3$	$-20$	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	$q-3\beta _{2}q^{3}+(1+2\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots$

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

$S_{4}^{\mathrm{old}}(84, [\chi]) \simeq$ $S_{4}^{\mathrm{new}}(7, [\chi])$$^{\oplus 6}$$\oplus$$S_{4}^{\mathrm{new}}(14, [\chi])$$^{\oplus 4}$$\oplus$$S_{4}^{\mathrm{new}}(21, [\chi])$$^{\oplus 3}$$\oplus$$S_{4}^{\mathrm{new}}(28, [\chi])$$^{\oplus 2}$$\oplus$$S_{4}^{\mathrm{new}}(42, [\chi])$$^{\oplus 2}$