Space of modular forms of level 3, weight 18, and trivial character

• Label: 3.18.a
• Level: $3$
• Weight: $18$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	7	3	4
Cusp forms	5	3	2
Eisenstein series	2	0	2

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
\(+\)	\(1\)
\(-\)	\(2\)

Trace form

\( 3 q + 798 q^{2} + 6561 q^{3} + 87060 q^{4} + 219306 q^{5} + 2558790 q^{6} + 3625008 q^{7} + 85352520 q^{8} + 129140163 q^{9} + O(q^{10}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(3))\) 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
3.18.a.a	$3$	$18$	3.a	1.a	$1$	$1$	$1$	$5.497$	\(\Q\)	None	✓	$1$	$1$	\(204\)	\(-6561\)	\(-163554\)	\(-20846560\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+204q^{2}-3^{8}q^{3}-89456q^{4}-163554q^{5}+\cdots\)
3.18.a.b	$3$	$18$	3.a	1.a	$1$	$2$	$2$	$5.497$	\(\Q(\sqrt{14569}) \)	None	✓	$1$	$0$	\(594\)	\(13122\)	\(382860\)	\(24471568\)		$-$	$-$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(297-\beta )q^{2}+3^{8}q^{3}+(88258-594\beta )q^{4}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)