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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(19\)	\(2\)	\(17\)		\(17\)	\(2\)	\(15\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(20\)	\(3\)	\(17\)		\(18\)	\(3\)	\(15\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(20\)	\(2\)	\(18\)		\(18\)	\(2\)	\(16\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(20\)	\(3\)	\(17\)		\(18\)	\(3\)	\(15\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(39\)	\(5\)	\(34\)		\(35\)	\(5\)	\(30\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(40\)	\(5\)	\(35\)		\(36\)	\(5\)	\(31\)		\(4\)	\(0\)	\(4\)

Trace form

10 * q + 167772160 * q^4 - 581301684 * q^5 - 10429506640 * q^7 + 2866670075904 * q^10 - 16662482272728 * q^11 + 152073991594940 * q^13 + 53123283025920 * q^14 + 2814749767106560 * q^16 + 3712895894871540 * q^17 + 31693425789499976 * q^19 - 9752623913631744 * q^20 - 61603721370009600 * q^22 - 60881013153792720 * q^23 - 285341441087651162 * q^25 - 424483544323325952 * q^26 - 174978085672714240 * q^28 - 5214605560819935588 * q^29 + 14225793791232015968 * q^31 + 32316293060577460224 * q^34 - 43378524843050553984 * q^35 - 30072691832188138180 * q^37 - 84683716229991628800 * q^38 + 48094743064177803264 * q^40 - 689669360396528418396 * q^41 + 268311501282557632760 * q^43 - 279550064185728565248 * q^44 + 108446894471536705536 * q^46 - 1193832408998047420800 * q^47 + 5264354963805457760634 * q^49 - 3603426344403532775424 * q^50 + 2551378204970492887040 * q^52 - 5621180137835037166260 * q^53 - 14710558735978028085168 * q^55 + 891260793954993438720 * q^56 - 3994145826562011955200 * q^58 + 38228821306859407257000 * q^59 - 32726834031630105304084 * q^61 + 23604184328588264079360 * q^62 + 47223664828696452136960 * q^64 + 177654708779457311978472 * q^65 - 34499683403570727419800 * q^67 + 62292056413773118832640 * q^68 - 242607367848435905200128 * q^70 + 139936441339392786163152 * q^71 - 339101461217586031608940 * q^73 - 209542101569708024659968 * q^74 + 531727450250411629346816 * q^76 - 1276076682116734140656640 * q^77 + 1156103285096642446730240 * q^79 - 163621877965765113544704 * q^80 - 146897549994473182986240 * q^82 - 2579042499519448031060520 * q^83 + 6227947887032585274320232 * q^85 - 655748401591199697076224 * q^86 - 1033538939828466981273600 * q^88 - 691982890500022036601436 * q^89 - 14710855485765731013572000 * q^91 - 1021413907980021682667520 * q^92 + 148954971790662045007872 * q^94 + 9607170614055271484156496 * q^95 - 573989268103632050742460 * q^97 + 12865016850176427121704960 * q^98

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	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
18.26.a.a	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓				6.26.a.c	$1$	$0$	\(-4096\)	\(0\)	\(799327650\)	\(7962409664\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+2^{24}q^{4}+799327650q^{5}+\cdots\)
18.26.a.b	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓				6.26.a.b	$1$	$1$	\(4096\)	\(0\)	\(-590425734\)	\(57857417576\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}-590425734q^{5}+\cdots\)
18.26.a.c	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓				2.26.a.a	$1$	$1$	\(4096\)	\(0\)	\(-341005350\)	\(-40882637368\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}-341005350q^{5}+\cdots\)
18.26.a.d	$18$	$26$	18.a	1.a	$1$	$1$	$1$	$71.279$	\(\Q\)	None	✓				6.26.a.a	$1$	$1$	\(4096\)	\(0\)	\(292754850\)	\(3580644032\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}+292754850q^{5}+\cdots\)
18.26.a.e	$18$	$26$	18.a	1.a	$1$	$2$	$2$	$71.279$	\(\Q(\sqrt{106705}) \)	None	✓		✓		2.26.a.b	$1$	$0$	\(-8192\)	\(0\)	\(-741953100\)	\(-376536944\)		$+$	$-$	$-$	$2^{7}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+2^{24}q^{4}+(-370976550+\cdots)q^{5}+\cdots\)
18.26.a.f	$18$	$26$	18.a	1.a	$1$	$2$	$2$	$71.279$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	18.26.a.f	$1$	$1$	\(-8192\)	\(0\)	\(-697960704\)	\(-19285401800\)		$+$	$+$	$+$	$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q-2^{12}q^{2}+2^{24}q^{4}+(-348980352+\cdots)q^{5}+\cdots\)
18.26.a.g	$18$	$26$	18.a	1.a	$1$	$2$	$2$	$71.279$	\(\mathbb{Q}[x]/(x^{2} - \cdots)\)	None	✓	✓	✓	✓	18.26.a.f	$1$	$0$	\(8192\)	\(0\)	\(697960704\)	\(-19285401800\)		$-$	$+$	$-$	$2^{5}\cdot 3^{4}$	$\mathrm{SU}(2)$	\(q+2^{12}q^{2}+2^{24}q^{4}+(348980352+\cdots)q^{5}+\cdots\)

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

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