Space of modular forms of level 9, weight 10, and Character 9.c

• Label: 9.10.c
• Level: $9$
• Weight: $10$
• Character orbit: 9.c
• Rep. character: $\chi_{9}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	9.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(9, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	16	16	0
Eisenstein series	4	4	0

Trace form

16 * q + 15 * q^2 - 3 * q^3 - 1793 * q^4 + 453 * q^5 + 2439 * q^6 - 343 * q^7 - 14478 * q^8 - 15669 * q^9 + 1020 * q^10 + 99150 * q^11 - 241212 * q^12 + 32435 * q^13 + 394824 * q^14 + 723843 * q^15 - 328193 * q^16 - 831078 * q^17 - 1039500 * q^18 - 170554 * q^19 + 1855164 * q^20 - 503475 * q^21 + 529359 * q^22 + 1064559 * q^23 - 2686059 * q^24 - 2293229 * q^25 + 2436312 * q^26 - 6176520 * q^27 + 1225724 * q^28 - 1309053 * q^29 + 30713544 * q^30 - 2359819 * q^31 + 5760063 * q^32 - 19931472 * q^33 + 981801 * q^34 - 31066554 * q^35 - 48894093 * q^36 + 16391516 * q^37 + 39490203 * q^38 + 74528535 * q^39 - 16760496 * q^40 + 54747318 * q^41 + 25242354 * q^42 + 15249608 * q^43 - 332509926 * q^44 - 139865967 * q^45 + 2390520 * q^46 + 156295545 * q^47 + 312045027 * q^48 + 15239583 * q^49 + 315590163 * q^50 + 3098385 * q^51 - 19773358 * q^52 - 525516228 * q^53 - 591710103 * q^54 - 7579770 * q^55 + 470339790 * q^56 + 581271465 * q^57 + 55408560 * q^58 + 307774074 * q^59 - 430082172 * q^60 + 69192125 * q^61 - 914436924 * q^62 - 693544725 * q^63 - 403588478 * q^64 + 482470359 * q^65 + 1912534074 * q^66 + 14328044 * q^67 + 915409575 * q^68 - 724756329 * q^69 - 229271934 * q^70 - 1239601392 * q^71 - 1729340037 * q^72 + 598613198 * q^73 + 1022736000 * q^74 + 1477690413 * q^75 + 119954093 * q^76 + 717995541 * q^77 + 243023958 * q^78 + 30257531 * q^79 - 2927826528 * q^80 - 1055378241 * q^81 - 202376022 * q^82 + 1176168291 * q^83 + 1383634866 * q^84 + 4818366 * q^85 + 1426944009 * q^86 + 617958567 * q^87 + 911312427 * q^88 - 3317041296 * q^89 - 981417492 * q^90 - 739230122 * q^91 - 76813998 * q^92 - 552731577 * q^93 - 1954316784 * q^94 - 391400652 * q^95 + 1854064512 * q^96 - 267311278 * q^97 + 4827300318 * q^98 + 1672014609 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(9, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
9.10.c.a	$9$	$10$	9.c	9.c	$3$	$16$	$8$	$4.635$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	9.10.c.a	$2$	$0$	\(15\)	\(-3\)	\(453\)	\(-343\)	$2^{14}\cdot 3^{28}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2+\beta _{2}-2\beta _{3})q^{2}+(9-18\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)