Space of modular forms of level 18, weight 4, and trivial character

• Label: 18.4.a
• Level: $18$
• Weight: $4$
• Character orbit: 18.a
• Rep. character: $\chi_{18}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	18.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(18))\).

	Total	New	Old
Modular forms	13	1	12
Cusp forms	5	1	4
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
\(-\)	\(-\)	\(+\)	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(0\)

Trace form

q + 2 * q^2 + 4 * q^4 - 6 * q^5 - 16 * q^7 + 8 * q^8 - 12 * q^10 - 12 * q^11 + 38 * q^13 - 32 * q^14 + 16 * q^16 + 126 * q^17 + 20 * q^19 - 24 * q^20 - 24 * q^22 - 168 * q^23 - 89 * q^25 + 76 * q^26 - 64 * q^28 - 30 * q^29 - 88 * q^31 + 32 * q^32 + 252 * q^34 + 96 * q^35 + 254 * q^37 + 40 * q^38 - 48 * q^40 - 42 * q^41 - 52 * q^43 - 48 * q^44 - 336 * q^46 + 96 * q^47 - 87 * q^49 - 178 * q^50 + 152 * q^52 - 198 * q^53 + 72 * q^55 - 128 * q^56 - 60 * q^58 + 660 * q^59 - 538 * q^61 - 176 * q^62 + 64 * q^64 - 228 * q^65 + 884 * q^67 + 504 * q^68 + 192 * q^70 - 792 * q^71 + 218 * q^73 + 508 * q^74 + 80 * q^76 + 192 * q^77 - 520 * q^79 - 96 * q^80 - 84 * q^82 + 492 * q^83 - 756 * q^85 - 104 * q^86 - 96 * q^88 - 810 * q^89 - 608 * q^91 - 672 * q^92 + 192 * q^94 - 120 * q^95 + 1154 * q^97 - 174 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(18))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
18.4.a.a	$18$	$4$	18.a	1.a	$1$	$1$	$1$	$1.062$	\(\Q\)	None	✓		✓	✓	6.4.a.a	$1$	$0$	\(2\)	\(0\)	\(-6\)	\(-16\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+4q^{4}-6q^{5}-2^{4}q^{7}+8q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(18)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)