Space of modular forms of level 18, weight 16, and trivial character

• Label: 18.16.a
• Level: $18$
• Weight: $16$
• Character orbit: 18.a
• Rep. character: $\chi_{18}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $6$
• Sturm bound: $48$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(48\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(18))\).

	Total	New	Old
Modular forms	49	6	43
Cusp forms	41	6	35
Eisenstein series	8	0	8

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

\(2\)	\(3\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(2\)
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(3\)
Minus space		\(-\)	\(3\)

Trace form

\( 6 q + 98304 q^{4} + 261144 q^{5} + 6924216 q^{7} + O(q^{10}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(18))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
18.16.a.a	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	$1$	$1$	\(-128\)	\(0\)	\(-77646\)	\(762104\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+2^{14}q^{4}-77646q^{5}+762104q^{7}+\cdots\)
18.16.a.b	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	$1$	$1$	\(-128\)	\(0\)	\(114810\)	\(-3034528\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+2^{14}q^{4}+114810q^{5}-3034528q^{7}+\cdots\)
18.16.a.c	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	$1$	$0$	\(-128\)	\(0\)	\(263040\)	\(3585764\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+2^{14}q^{4}+263040q^{5}+3585764q^{7}+\cdots\)
18.16.a.d	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	$1$	$1$	\(128\)	\(0\)	\(-263040\)	\(3585764\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+2^{14}q^{4}-263040q^{5}+3585764q^{7}+\cdots\)
18.16.a.e	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	$1$	$0$	\(128\)	\(0\)	\(-90510\)	\(56\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+2^{14}q^{4}-90510q^{5}+56q^{7}+\cdots\)
18.16.a.f	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	$1$	$0$	\(128\)	\(0\)	\(314490\)	\(2025056\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+2^{14}q^{4}+314490q^{5}+2025056q^{7}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)