Space of modular forms of level 21, weight 18, and Character 21.g

• Label: 21.18.g
• Level: $21$
• Weight: $18$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $86$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$21 = 3 \cdot 7$
Weight:	$k$	$=$	$18$
Character orbit:	$[\chi]$	$=$	21.g (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$48$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{18}(21, [\chi])$.

	Total	New	Old
Modular forms	94	94	0
Cusp forms	86	86	0
Eisenstein series	8	8	0

Trace form

86 * q - 3 * q^3 + 2621438 * q^4 - 7098699 * q^7 + 30469167 * q^9 + 465470970 * q^10 - 5071654704 * q^12 - 7104382296 * q^15 - 127639474314 * q^16 - 14553542550 * q^18 + 150097298991 * q^19 + 374239010916 * q^21 - 832496305460 * q^22 - 1354439880378 * q^24 - 6436929145345 * q^25 - 4120737341762 * q^28 + 284772818082 * q^30 + 11445560805771 * q^31 - 18426553023870 * q^33 - 39859913080524 * q^36 + 4444131806949 * q^37 + 101376443242071 * q^39 + 52009146351690 * q^40 + 273411312457290 * q^42 + 153014512996230 * q^43 - 463828715581158 * q^45 - 691873824309656 * q^46 - 299001462932059 * q^49 + 123926983295328 * q^51 - 930289519449696 * q^52 + 528953393499678 * q^54 - 4643419536509382 * q^57 + 521920547533210 * q^58 - 416477060451846 * q^60 - 11235030059336640 * q^61 - 10550026068854145 * q^63 + 5557536420030492 * q^64 + 21705058495057878 * q^66 + 3908694716672869 * q^67 + 44463964567209810 * q^70 + 7798479140884800 * q^72 - 16731485430446037 * q^73 + 32273278987450665 * q^75 - 67997864561346840 * q^78 - 4800167576088071 * q^79 + 27456234084598923 * q^81 + 4877409168868320 * q^82 + 51820313503653696 * q^84 + 2464288230356616 * q^85 - 61426317616508880 * q^87 - 112618869011616970 * q^88 - 75207200976552951 * q^91 + 46647692308142505 * q^93 + 248077621213302516 * q^94 - 363875964512101146 * q^96 + 303894121197814080 * q^99

Decomposition of $S_{18}^{\mathrm{new}}(21, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.18.g.a	$21$	$18$	21.g	21.g	$6$	$2$	$1$	$38.477$	$\Q(\sqrt{-3})$	$\Q(\sqrt{-3})$		✓			21.18.g.a	$4$	$0$	$0$	$19683$	$0$	$-2758181$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+(3^{8}+3^{8}\zeta_{6})q^{3}+(-2^{17}+2^{17}\zeta_{6})q^{4}+\cdots$
21.18.g.b	$21$	$18$	21.g	21.g	$6$	$84$	$42$	$38.477$		None		✓	✓		21.18.g.b	$4$	$0$	$0$	$-19686$	$0$	$-4340518$		$\mathrm{SU}(2)[C_{6}]$