Space of modular forms of level 27, weight 10, and trivial character

• Label: 27.10.a
• Level: $27$
• Weight: $10$
• Character orbit: 27.a
• Rep. character: $\chi_{27}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(27))\).

	Total	New	Old
Modular forms	30	12	18
Cusp forms	24	12	12
Eisenstein series	6	0	6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	Dim
\(+\)	\(5\)
\(-\)	\(7\)

Trace form

\( 12 q + 3414 q^{4} + 2940 q^{7} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(27))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
27.10.a.a	$27$	$10$	27.a	1.a	$1$	$2$	$2$	$13.906$	\(\Q(\sqrt{14}) \)	None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-1526\)		$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-8q^{4}-22\beta q^{5}-763q^{7}+\cdots\)
27.10.a.b	$27$	$10$	27.a	1.a	$1$	$3$	$3$	$13.906$	3.3.177113.1	None	✓	$1$	$0$	\(-3\)	\(0\)	\(1983\)	\(-3693\)		$-$	$-$	$2\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{2}+(199-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
27.10.a.c	$27$	$10$	27.a	1.a	$1$	$3$	$3$	$13.906$	3.3.177113.1	None	✓	$1$	$1$	\(3\)	\(0\)	\(-1983\)	\(-3693\)		$+$	$+$	$2\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{2}+(199-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
27.10.a.d	$27$	$10$	27.a	1.a	$1$	$4$	$4$	$13.906$	4.4.203942560.1	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(11852\)		$-$	$-$	$2^{3}\cdot 3^{8}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(559+\beta _{3})q^{4}+(-10\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(27))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(27)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)