Space of modular forms of level 27, weight 10, and Character 27.e

• Label: 27.10.e
• Level: $27$
• Weight: $10$
• Character orbit: 27.e
• Rep. character: $\chi_{27}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $156$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(27, [\chi])\).

	Total	New	Old
Modular forms	168	168	0
Cusp forms	156	156	0
Eisenstein series	12	12	0

Trace form

156 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 2382 * q^5 - 6822 * q^6 - 6 * q^7 + 36861 * q^8 + 2538 * q^9 - 3 * q^10 - 121767 * q^11 + 319935 * q^12 - 6 * q^13 - 720417 * q^14 - 706356 * q^15 + 1530 * q^16 + 1002249 * q^17 + 922437 * q^18 - 3 * q^19 - 8448573 * q^20 - 3497394 * q^21 - 1585014 * q^22 + 9316482 * q^23 + 7959258 * q^24 + 2192178 * q^25 - 33129678 * q^26 - 3148155 * q^27 - 12 * q^28 + 19657236 * q^29 + 21174507 * q^30 - 4633692 * q^31 - 37550952 * q^32 - 19055889 * q^33 + 14341770 * q^34 + 34449663 * q^35 + 137733552 * q^36 - 3 * q^37 - 92022060 * q^38 - 89330160 * q^39 + 6645801 * q^40 - 33127221 * q^41 + 227141658 * q^42 + 2356203 * q^43 + 1001541 * q^44 - 78992532 * q^45 - 3 * q^46 - 33488952 * q^47 + 248865393 * q^48 - 93214644 * q^49 - 72027753 * q^50 - 101541537 * q^51 + 160531713 * q^52 + 4841352 * q^53 - 315431874 * q^54 - 12 * q^55 - 91770981 * q^56 - 103852992 * q^57 - 320682489 * q^58 + 538090854 * q^59 + 1127571210 * q^60 + 36683436 * q^61 - 55862958 * q^62 - 419972706 * q^63 - 956301315 * q^64 - 852347310 * q^65 + 472205277 * q^66 - 109026897 * q^67 - 508886217 * q^68 - 1234413090 * q^69 - 815297649 * q^70 + 940878639 * q^71 + 2831326452 * q^72 - 221849931 * q^73 + 838884579 * q^74 - 226667796 * q^75 + 908401146 * q^76 - 967811358 * q^77 - 1247881230 * q^78 - 1228059150 * q^79 - 2497115154 * q^80 - 392600970 * q^81 - 12 * q^82 - 297703284 * q^83 + 1027656618 * q^84 + 1535949369 * q^85 + 2930201574 * q^86 + 2687612040 * q^87 + 2837227002 * q^88 + 1774997208 * q^89 + 7127326206 * q^90 + 551343507 * q^91 - 6896645517 * q^92 - 7299151842 * q^93 + 414852915 * q^94 - 9000269169 * q^95 - 2644638174 * q^96 + 3371772333 * q^97 + 6901039926 * q^98 + 5248107342 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.10.e.a	$27$	$10$	27.e	27.e	$9$	$156$	$26$	$13.906$		None		✓	✓	✓	27.10.e.a	$2$	$0$	\(-6\)	\(-6\)	\(2382\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$