Space of modular forms of level 27, weight 8, and Character 27.c

• Label: 27.8.c
• Level: $27$
• Weight: $8$
• Character orbit: 27.c
• Rep. character: $\chi_{27}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(27, [\chi])\).

	Total	New	Old
Modular forms	48	16	32
Cusp forms	36	12	24
Eisenstein series	12	4	8

Trace form

12 * q + 9 * q^2 - 321 * q^4 + 180 * q^5 - 84 * q^7 - 5922 * q^8 + 252 * q^10 + 8460 * q^11 - 1848 * q^13 + 16272 * q^14 - 12417 * q^16 - 30564 * q^17 + 24432 * q^19 + 40788 * q^20 - 35001 * q^22 + 51588 * q^23 + 4746 * q^25 - 536472 * q^26 + 75516 * q^28 + 414648 * q^29 + 8196 * q^31 + 1048977 * q^32 - 106623 * q^34 - 2210616 * q^35 + 139344 * q^37 + 1952685 * q^38 + 305496 * q^40 + 1731582 * q^41 + 408372 * q^43 - 5169114 * q^44 - 1684008 * q^46 + 1631484 * q^47 - 179010 * q^49 + 1654461 * q^50 + 681594 * q^52 - 2835648 * q^53 - 16056 * q^55 + 1784466 * q^56 - 948384 * q^58 + 2055636 * q^59 - 2723196 * q^61 + 1026828 * q^62 + 7178178 * q^64 + 1387620 * q^65 + 3806556 * q^67 - 2142639 * q^68 + 953442 * q^70 - 2408400 * q^71 - 10670052 * q^73 - 9846504 * q^74 - 6727827 * q^76 - 3478824 * q^77 + 6020916 * q^79 + 38072448 * q^80 + 9403002 * q^82 - 9605052 * q^83 - 1698624 * q^85 - 34278561 * q^86 - 16459029 * q^88 + 24630264 * q^89 + 13570104 * q^91 - 39143394 * q^92 + 12602808 * q^94 - 10422072 * q^95 + 9977226 * q^97 + 95833314 * q^98

Decomposition of \(S_{8}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.8.c.a	$27$	$8$	27.c	9.c	$3$	$12$	$6$	$8.434$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None			✓	✓	9.8.c.a	$2$	$0$	\(9\)	\(0\)	\(180\)	\(-84\)	$2^{8}\cdot 3^{21}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{6}+\beta _{7})q^{2}+(-52+3\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)