Space of modular forms of level 7, weight 18, and Character 7.c

• Label: 7.18.c
• Level: $7$
• Weight: $18$
• Character orbit: 7.c
• Rep. character: $\chi_{7}(2,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(7, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	20	20	0
Eisenstein series	4	4	0

Trace form

20 * q + 270 * q^2 + 6560 * q^3 - 551660 * q^4 + 1089798 * q^5 - 1687556 * q^6 + 14395360 * q^7 - 237823200 * q^8 - 498883228 * q^9 + 222553738 * q^10 - 148256184 * q^11 + 2808533140 * q^12 + 3578734040 * q^13 + 25683984606 * q^14 - 26900793736 * q^15 - 50209759472 * q^16 + 15259176570 * q^17 + 81764237020 * q^18 - 71656970872 * q^19 - 180641544216 * q^20 - 669146889614 * q^21 + 1499692748380 * q^22 - 316306503180 * q^23 + 694489934496 * q^24 + 591325905568 * q^25 + 4488505674324 * q^26 - 11473086373360 * q^27 + 2858273469380 * q^28 + 284876854680 * q^29 - 9357829097258 * q^30 - 1607821082076 * q^31 + 18893460602400 * q^32 + 9589772011550 * q^33 - 32628298247940 * q^34 - 103506510744 * q^35 + 76724663114416 * q^36 + 5528585266950 * q^37 - 15690283928010 * q^38 + 28451541414128 * q^39 - 91022360866896 * q^40 - 66727631114424 * q^41 - 74393390286880 * q^42 - 93028396916240 * q^43 + 162849953080692 * q^44 + 8592264491540 * q^45 - 563088234018354 * q^46 + 162460135616460 * q^47 + 1626223055746720 * q^48 + 37188390461684 * q^49 - 156105592028976 * q^50 - 41571323179104 * q^51 - 664578572037800 * q^52 + 349838159677350 * q^53 - 2197621449925058 * q^54 - 630210277345912 * q^55 - 3391192609585536 * q^56 + 3387478208982380 * q^57 + 1117009291618900 * q^58 + 2898325666051656 * q^59 + 1851302466771436 * q^60 + 4829263771794542 * q^61 - 12440234322280740 * q^62 + 1252577979478000 * q^63 + 2254847316158720 * q^64 + 2323606775562324 * q^65 + 7963993945620406 * q^66 + 1327703510619200 * q^67 + 570001815036780 * q^68 - 19909363410939516 * q^69 - 17777971289904490 * q^70 + 15480661755189216 * q^71 + 16233423509033760 * q^72 - 3163858704730590 * q^73 - 4018632851551110 * q^74 - 8119026314209112 * q^75 - 14641245177256376 * q^76 - 46825571816043510 * q^77 + 48702643123708840 * q^78 + 40826108816616316 * q^79 + 90814104963906864 * q^80 - 69159481630723930 * q^81 + 21247223257167740 * q^82 + 10623055038659280 * q^83 - 178832833754555092 * q^84 + 51769432859611308 * q^85 + 113956439761484328 * q^86 + 171557044814594000 * q^87 - 117726124940340000 * q^88 + 31115179936936434 * q^89 - 503037784464315176 * q^90 - 219799610507722112 * q^91 + 208501803198310920 * q^92 + 257332309943680890 * q^93 + 405400048855155726 * q^94 - 22431094320108540 * q^95 + 232620528206160416 * q^96 - 702800336503765080 * q^97 - 760473415304075970 * q^98 + 928280307128172080 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(7, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7.18.c.a	$7$	$18$	7.c	7.c	$3$	$20$	$10$	$12.826$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	7.18.c.a	$2$	$0$	\(270\)	\(6560\)	\(1089798\)	\(14395360\)	$2^{50}\cdot 3^{18}\cdot 7^{19}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+3^{3}\beta _{2})q^{2}+(656-656\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)