Space of modular forms of level 27, weight 4, and Character 27.c

• Label: 27.4.c
• Level: $27$
• Weight: $4$
• Character orbit: 27.c
• Rep. character: $\chi_{27}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(27, [\chi])\).

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

Trace form

4 * q + 3 * q^2 - 5 * q^4 + 15 * q^5 - 7 * q^7 - 66 * q^8 + 12 * q^10 + 66 * q^11 + 11 * q^13 + 60 * q^14 + 7 * q^16 - 198 * q^17 - 154 * q^19 - 12 * q^20 + 33 * q^22 + 33 * q^23 + 121 * q^25 + 528 * q^26 + 332 * q^28 - 51 * q^29 - 43 * q^31 - 423 * q^32 - 297 * q^34 - 6 * q^35 - 100 * q^37 - 561 * q^38 - 264 * q^40 + 132 * q^41 - 88 * q^43 + 462 * q^44 - 528 * q^46 + 399 * q^47 + 513 * q^49 - 429 * q^50 + 770 * q^52 - 108 * q^53 + 1254 * q^55 + 66 * q^56 + 60 * q^58 + 798 * q^59 - 439 * q^61 - 228 * q^62 - 1454 * q^64 + 165 * q^65 - 988 * q^67 + 693 * q^68 - 318 * q^70 - 2736 * q^71 - 910 * q^73 + 816 * q^74 + 1529 * q^76 - 165 * q^77 + 803 * q^79 - 192 * q^80 + 3630 * q^82 + 813 * q^83 - 594 * q^85 + 33 * q^86 - 1221 * q^88 + 792 * q^89 - 1562 * q^91 - 858 * q^92 - 2100 * q^94 - 132 * q^95 - 736 * q^97 + 846 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.4.c.a	$27$	$4$	27.c	9.c	$3$	$4$	$2$	$1.593$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None			✓	✓	9.4.c.a	$2$	$0$	\(3\)	\(0\)	\(15\)	\(-7\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-4+\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)