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

• Label: 27.10.c
• Level: $27$
• Weight: $10$
• Character orbit: 27.c
• Rep. character: $\chi_{27}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(30\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	60	20	40
Cusp forms	48	16	32
Eisenstein series	12	4	8

Trace form

\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.10.c.a	$27$	$10$	27.c	9.c	$3$	$16$	$8$	$13.906$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-15\)	\(0\)	\(-453\)	\(-343\)	$2^{14}\cdot 3^{40}\cdot 17^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\beta _{8}+2\beta _{9})q^{2}+(2\beta _{1}-2\beta _{8}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)