Space of modular forms of level 18, weight 6, and trivial character

• Label: 18.6.a
• Level: $18$
• Weight: $6$
• Character orbit: 18.a
• Rep. character: $\chi_{18}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $18$
• Trace bound: $5$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(18))\).

	Total	New	Old
Modular forms	19	3	16
Cusp forms	11	3	8
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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(4\)	\(1\)	\(3\)		\(2\)	\(1\)	\(1\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(5\)	\(1\)	\(4\)		\(3\)	\(1\)	\(2\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(5\)	\(1\)	\(4\)		\(3\)	\(1\)	\(2\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(5\)	\(0\)	\(5\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(9\)	\(1\)	\(8\)		\(5\)	\(1\)	\(4\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(10\)	\(2\)	\(8\)		\(6\)	\(2\)	\(4\)		\(4\)	\(0\)	\(4\)

Trace form

3 * q - 4 * q^2 + 48 * q^4 + 66 * q^5 - 120 * q^7 - 64 * q^8 + 504 * q^10 + 60 * q^11 - 1326 * q^13 - 704 * q^14 + 768 * q^16 + 414 * q^17 - 372 * q^19 + 1056 * q^20 - 3312 * q^22 - 600 * q^23 + 13413 * q^25 + 2632 * q^26 - 1920 * q^28 - 5574 * q^29 - 12720 * q^31 - 1024 * q^32 - 6264 * q^34 + 11616 * q^35 + 3138 * q^37 - 3824 * q^38 + 8064 * q^40 - 19194 * q^41 - 16428 * q^43 + 960 * q^44 + 33120 * q^46 + 19680 * q^47 + 24363 * q^49 - 4924 * q^50 - 21216 * q^52 + 31266 * q^53 - 69768 * q^55 - 11264 * q^56 + 21528 * q^58 - 26340 * q^59 + 54474 * q^61 + 14368 * q^62 + 12288 * q^64 - 43428 * q^65 + 56508 * q^67 + 6624 * q^68 - 160128 * q^70 - 6120 * q^71 - 59178 * q^73 + 33832 * q^74 - 5952 * q^76 + 10560 * q^77 + 130560 * q^79 + 16896 * q^80 + 130536 * q^82 + 6468 * q^83 - 83268 * q^85 - 53264 * q^86 - 52992 * q^88 + 32742 * q^89 - 16944 * q^91 - 9600 * q^92 + 74880 * q^94 + 63096 * q^95 + 106206 * q^97 - 56676 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(18))\) 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
18.6.a.a	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	\(\Q\)	None	✓	✓	✓	✓	18.6.a.a	$1$	$1$	\(-4\)	\(0\)	\(-96\)	\(-148\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}-96q^{5}-148q^{7}+\cdots\)
18.6.a.b	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	\(\Q\)	None	✓		✓	✓	6.6.a.a	$1$	$0$	\(-4\)	\(0\)	\(66\)	\(176\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{2}+2^{4}q^{4}+66q^{5}+176q^{7}+\cdots\)
18.6.a.c	$18$	$6$	18.a	1.a	$1$	$1$	$1$	$2.887$	\(\Q\)	None	✓	✓	✓	✓	18.6.a.a	$1$	$0$	\(4\)	\(0\)	\(96\)	\(-148\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{2}+2^{4}q^{4}+96q^{5}-148q^{7}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(18))\) into lower level spaces

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