Space of modular forms of level 21, weight 10, and Character 21.g

• Label: 21.10.g
• Level: $21$
• Weight: $10$
• Character orbit: 21.g
• Rep. character: $\chi_{21}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $1$
• Sturm bound: $26$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$21 = 3 \cdot 7$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	21.g (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$26$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{10}(21, [\chi])$.

	Total	New	Old
Modular forms	52	52	0
Cusp forms	44	44	0
Eisenstein series	8	8	0

Trace form

44 * q - 3 * q^3 + 5118 * q^4 - 7504 * q^7 + 17745 * q^9 + 76890 * q^10 + 81456 * q^12 - 641226 * q^15 - 1273994 * q^16 + 625962 * q^18 - 1139244 * q^19 - 1975575 * q^21 + 5549324 * q^22 + 6080166 * q^24 - 4598110 * q^25 + 10605630 * q^28 - 1382718 * q^30 - 22882362 * q^31 - 3156399 * q^33 + 31195572 * q^36 - 4456592 * q^37 - 14655018 * q^39 + 12460170 * q^40 - 11421942 * q^42 - 85822628 * q^43 + 79227387 * q^45 + 49095272 * q^46 + 166680584 * q^49 - 96309261 * q^51 - 377398368 * q^52 + 467859294 * q^54 + 32445198 * q^57 - 16267846 * q^58 - 610675686 * q^60 - 363974514 * q^61 - 719829369 * q^63 - 347640676 * q^64 + 1519139574 * q^66 + 535490032 * q^67 + 2211763890 * q^70 - 273084960 * q^72 - 1648617900 * q^73 + 1003442430 * q^75 + 665477544 * q^78 - 3774974 * q^79 - 1629744543 * q^81 - 934228512 * q^82 - 4679949120 * q^84 - 2278350084 * q^85 + 3033912798 * q^87 + 4079405878 * q^88 + 4495764294 * q^91 - 713608743 * q^93 - 6593180172 * q^94 + 2822228262 * q^96 + 1832627190 * q^99

Decomposition of $S_{10}^{\mathrm{new}}(21, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
21.10.g.a	$21$	$10$	21.g	21.g	$6$	$44$	$22$	$10.816$		None		✓	✓	✓	21.10.g.a	$4$	$0$	$0$	$-3$	$0$	$-7504$		$\mathrm{SU}(2)[C_{6}]$