Space of modular forms of level 18, weight 26, and trivial character

• Label: 18.26.a
• Level: $18$
• Weight: $26$
• Character orbit: 18.a
• Rep. character: $\chi_{18}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $7$
• Sturm bound: $78$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(78\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(18))\).

	Total	New	Old
Modular forms	79	10	69
Cusp forms	71	10	61
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
\(+\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(2\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(5\)
Minus space		\(-\)	\(5\)

Trace form

\( 10 q + 167772160 q^{4} - 581301684 q^{5} - 10429506640 q^{7} + O(q^{10}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.26.a.a	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓	$1$	$0$	\(-4096\)	\(0\)	\(799327650\)	\(7962409664\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+2^{24}q^{4}+799327650q^{5}+\cdots\)
18.26.a.b	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓	$1$	$1$	\(4096\)	\(0\)	\(-590425734\)	\(57857417576\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}-590425734q^{5}+\cdots\)
18.26.a.c	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓	$1$	$1$	\(4096\)	\(0\)	\(-341005350\)	\(-40882637368\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}-341005350q^{5}+\cdots\)
18.26.a.d	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓	$1$	$1$	\(4096\)	\(0\)	\(292754850\)	\(3580644032\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}+292754850q^{5}+\cdots\)
18.26.a.e	$18$	$26$	18.a	1.a	$1$	$2$	$2$	$71.279$	\(\Q(\sqrt{106705}) \)	None	✓	$1$	$0$	\(-8192\)	\(0\)	\(-741953100\)	\(-376536944\)		$+$	$-$	$-$	$2^{7}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+2^{24}q^{4}+(-370976550+\cdots)q^{5}+\cdots\)
18.26.a.f	$18$	$26$	18.a	1.a	$1$	$2$	$2$	$71.279$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$1$	\(-8192\)	\(0\)	\(-697960704\)	\(-19285401800\)		$+$	$+$	$+$	$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+2^{24}q^{4}+(-348980352+\cdots)q^{5}+\cdots\)
18.26.a.g	$18$	$26$	18.a	1.a	$1$	$2$	$2$	$71.279$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	$1$	$0$	\(8192\)	\(0\)	\(697960704\)	\(-19285401800\)		$-$	$+$	$-$	$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}+(348980352+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(18)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)