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

• Label: 27.5.b
• Level: $27$
• Weight: $5$
• Character orbit: 27.b
• Rep. character: $\chi_{27}(26,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $15$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(15\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	15	5	10
Cusp forms	9	5	4
Eisenstein series	6	0	6

Trace form

5 * q - 46 * q^4 + 67 * q^7 - 414 * q^10 + 457 * q^13 + 1226 * q^16 - 791 * q^19 - 1638 * q^22 + 515 * q^25 - 422 * q^28 + 2572 * q^31 - 2052 * q^34 - 1403 * q^37 + 198 * q^40 - 2318 * q^43 + 14544 * q^46 - 5664 * q^49 - 8384 * q^52 + 3366 * q^55 + 684 * q^58 + 3685 * q^61 - 9922 * q^64 + 19141 * q^67 + 90 * q^70 - 25361 * q^73 - 29756 * q^76 - 5675 * q^79 + 32904 * q^82 + 18252 * q^85 + 69246 * q^88 - 32173 * q^91 - 10116 * q^94 - 9581 * q^97

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.b.a	$27$	$5$	27.b	3.b	$2$	$1$	$1$	$2.791$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			27.5.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(71\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}+71q^{7}-337q^{13}+2^{8}q^{16}+\cdots\)
27.5.b.b	$27$	$5$	27.b	3.b	$2$	$2$	$2$	$2.791$	\(\Q(\sqrt{-6}) \)	None		✓			27.5.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(34\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-38q^{4}+2\beta q^{5}+17q^{7}-22\beta q^{8}+\cdots\)
27.5.b.c	$27$	$5$	27.b	3.b	$2$	$2$	$2$	$2.791$	\(\Q(\sqrt{-1}) \)	None		✓			27.5.b.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-38\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}+7 q^{4}+11\beta q^{5}-19 q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)