Space of modular forms of level 27, weight 5, and Character 27.f

• Label: 27.5.f
• Level: $27$
• Weight: $5$
• Character orbit: 27.f
• Rep. character: $\chi_{27}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $66$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(27, [\chi])\).

	Total	New	Old
Modular forms	78	78	0
Cusp forms	66	66	0
Eisenstein series	12	12	0

Trace form

66 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 3 * q^5 + 90 * q^6 - 6 * q^7 - 9 * q^8 - 108 * q^9 - 3 * q^10 - 492 * q^11 - 339 * q^12 - 6 * q^13 + 1137 * q^14 + 1017 * q^15 - 54 * q^16 - 9 * q^17 + 603 * q^18 - 3 * q^19 - 2487 * q^20 - 2784 * q^21 + 1002 * q^22 - 2724 * q^23 - 3312 * q^24 + 435 * q^25 + 1368 * q^27 - 12 * q^28 + 5016 * q^29 + 10773 * q^30 - 1671 * q^31 + 10224 * q^32 + 2925 * q^33 - 342 * q^34 - 2682 * q^35 - 7704 * q^36 - 3 * q^37 - 6564 * q^38 - 1983 * q^39 - 1113 * q^40 + 5754 * q^41 + 8694 * q^42 - 1266 * q^43 - 4545 * q^44 - 7029 * q^45 - 3 * q^46 - 9159 * q^47 - 28383 * q^48 + 5898 * q^49 - 34977 * q^50 - 14814 * q^51 + 2871 * q^52 + 13878 * q^54 - 12 * q^55 + 39243 * q^56 + 15792 * q^57 - 12291 * q^58 + 24762 * q^59 + 50670 * q^60 - 8358 * q^61 + 38304 * q^62 + 21609 * q^63 + 6141 * q^64 + 23727 * q^65 + 11349 * q^66 + 15996 * q^67 - 43533 * q^68 - 26847 * q^69 - 7251 * q^70 - 19773 * q^71 - 77580 * q^72 + 6108 * q^73 - 74847 * q^74 - 49155 * q^75 - 28614 * q^76 - 33909 * q^77 - 9108 * q^78 - 5658 * q^79 - 12600 * q^81 - 12 * q^82 + 18813 * q^83 + 82356 * q^84 + 24219 * q^85 + 96474 * q^86 + 84555 * q^87 + 36042 * q^88 + 110232 * q^89 + 153540 * q^90 - 6042 * q^91 + 73545 * q^92 + 1293 * q^93 + 2631 * q^94 - 65163 * q^95 - 152226 * q^96 - 3696 * q^97 - 259938 * q^98 - 162405 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.5.f.a	$27$	$5$	27.f	27.f	$18$	$66$	$11$	$2.791$		None		✓	✓	✓	27.5.f.a	$2$	$0$	\(-6\)	\(-6\)	\(3\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$