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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(13\)	\(1\)	\(12\)		\(11\)	\(1\)	\(10\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(12\)	\(2\)	\(10\)		\(10\)	\(2\)	\(8\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(12\)	\(1\)	\(11\)		\(10\)	\(1\)	\(9\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(12\)	\(2\)	\(10\)		\(10\)	\(2\)	\(8\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(25\)	\(3\)	\(22\)		\(21\)	\(3\)	\(18\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(24\)	\(3\)	\(21\)		\(20\)	\(3\)	\(17\)		\(4\)	\(0\)	\(4\)

Trace form

6 * q + 98304 * q^4 + 261144 * q^5 + 6924216 * q^7 - 43425792 * q^10 + 41075424 * q^11 - 254112756 * q^13 + 550084608 * q^14 + 1610612736 * q^16 + 5461900632 * q^17 - 5167009968 * q^19 + 4278583296 * q^20 - 25768304640 * q^22 - 2612038752 * q^23 + 81580872066 * q^25 - 23615815680 * q^26 + 113446354944 * q^28 - 257198248296 * q^29 - 408938462664 * q^31 - 156675686400 * q^34 + 229286306016 * q^35 + 1636049157492 * q^37 + 884208918528 * q^38 - 711488176128 * q^40 + 2048853252600 * q^41 - 4873382203632 * q^43 + 672979746816 * q^44 + 1481812180992 * q^46 - 9705384160416 * q^47 + 11120052363606 * q^49 + 11249380196352 * q^50 - 4163383394304 * q^52 - 25540321761864 * q^53 + 6844247235072 * q^55 + 9012586217472 * q^56 - 21753679896576 * q^58 - 32598503680320 * q^59 - 23063727716700 * q^61 + 96763632279552 * q^62 + 26388279066624 * q^64 - 11084081113008 * q^65 + 96029925375072 * q^67 + 89487779954688 * q^68 - 107772857008128 * q^70 - 135158267441376 * q^71 - 30680860304652 * q^73 + 251213352763392 * q^74 - 84656291315712 * q^76 - 573783871269312 * q^77 - 32535586725000 * q^79 + 70100308721664 * q^80 + 307010001125376 * q^82 - 374096416055328 * q^83 + 737242480903824 * q^85 + 444207160664064 * q^86 - 422187903221760 * q^88 + 285108615969048 * q^89 - 898479641616528 * q^91 - 42795642912768 * q^92 - 742495624740864 * q^94 + 1362054542256000 * q^95 - 520503457299612 * q^97 - 728103793065984 * q^98

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	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
18.16.a.a	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓				6.16.a.c	$1$	$1$	\(-128\)	\(0\)	\(-77646\)	\(762104\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+2^{14}q^{4}-77646q^{5}+762104q^{7}+\cdots\)
18.16.a.b	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓				6.16.a.b	$1$	$1$	\(-128\)	\(0\)	\(114810\)	\(-3034528\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+2^{14}q^{4}+114810q^{5}-3034528q^{7}+\cdots\)
18.16.a.c	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	✓	✓	✓	18.16.a.c	$1$	$0$	\(-128\)	\(0\)	\(263040\)	\(3585764\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2^{7}q^{2}+2^{14}q^{4}+263040q^{5}+3585764q^{7}+\cdots\)
18.16.a.d	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓	✓	✓	✓	18.16.a.c	$1$	$1$	\(128\)	\(0\)	\(-263040\)	\(3585764\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+2^{14}q^{4}-263040q^{5}+3585764q^{7}+\cdots\)
18.16.a.e	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓				2.16.a.a	$1$	$0$	\(128\)	\(0\)	\(-90510\)	\(56\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+2^{14}q^{4}-90510q^{5}+56q^{7}+\cdots\)
18.16.a.f	$18$	$16$	18.a	1.a	$1$	$1$	$1$	$25.685$	\(\Q\)	None	✓				6.16.a.a	$1$	$0$	\(128\)	\(0\)	\(314490\)	\(2025056\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{7}q^{2}+2^{14}q^{4}+314490q^{5}+2025056q^{7}+\cdots\)

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

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