Space of modular forms of level 1, weight 18, and trivial character

• Label: 1.18.a
• Level: $1$
• Weight: $18$
• Character orbit: 1.a
• Rep. character: $\chi_{1}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $1$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(1\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(1))\).

	Total	New	Old
Modular forms	2	2	0
Cusp forms	1	1	0
Eisenstein series	1	1	0

Trace form

q - 528 * q^2 - 4284 * q^3 + 147712 * q^4 - 1025850 * q^5 + 2261952 * q^6 + 3225992 * q^7 - 8785920 * q^8 - 110787507 * q^9 + 541648800 * q^10 - 753618228 * q^11 - 632798208 * q^12 + 2541064526 * q^13 - 1703323776 * q^14 + 4394741400 * q^15 - 14721941504 * q^16 - 5429742318 * q^17 + 58495803696 * q^18 + 1487499860 * q^19 - 151530355200 * q^20 - 13820149728 * q^21 + 397910424384 * q^22 - 317091823464 * q^23 + 37638881280 * q^24 + 289428769375 * q^25 - 1341682069728 * q^26 + 1027850138280 * q^27 + 476517730304 * q^28 + 2433410602590 * q^29 - 2320423459200 * q^30 - 8849722053088 * q^31 + 8924773220352 * q^32 + 3228500488752 * q^33 + 2866903943904 * q^34 - 3309383893200 * q^35 - 16364644233984 * q^36 + 12691652946662 * q^37 - 785399926080 * q^38 - 10885920429384 * q^39 + 9013036032000 * q^40 + 48864151002282 * q^41 + 7297039056384 * q^42 - 91019974317844 * q^43 - 111318455694336 * q^44 + 113651364055950 * q^45 + 167424482788992 * q^46 - 49304994276048 * q^47 + 63068797403136 * q^48 - 222223489603143 * q^49 - 152818390230000 * q^50 + 23261016090312 * q^51 + 375345723264512 * q^52 + 22940453195766 * q^53 - 542704873011840 * q^54 + 773099259193800 * q^55 - 28343307632640 * q^56 - 6372449400240 * q^57 - 1284840798167520 * q^58 + 32695090729980 * q^59 + 649156041676800 * q^60 - 1308285854869378 * q^61 + 4672653244030464 * q^62 - 357399611281944 * q^63 - 2782645943533568 * q^64 - 2606751043997100 * q^65 - 1704648258061056 * q^66 + 5196143861984132 * q^67 - 802038097276416 * q^68 + 1358421371719776 * q^69 + 1747354695609600 * q^70 - 3709489877412408 * q^71 + 973370173501440 * q^72 + 3402372968272586 * q^73 - 6701192755837536 * q^74 - 1239912848002500 * q^75 + 219721579320320 * q^76 - 2431166374582176 * q^77 + 5747765986714752 * q^78 + 2366533941308240 * q^79 + 15102503691878400 * q^80 + 9903806719952121 * q^81 - 25800271729204896 * q^82 - 29766750443172204 * q^83 - 2041401956622336 * q^84 + 5570101156920300 * q^85 + 48058546439821632 * q^86 - 10424731021495560 * q^87 + 6621229461749760 * q^88 + 29167184100574170 * q^89 - 60007920221541600 * q^90 + 8197453832359792 * q^91 - 46838267427514368 * q^92 + 37912209275428992 * q^93 + 26033036977753344 * q^94 - 1525951731381000 * q^95 - 38233728475987968 * q^96 - 63769879140957598 * q^97 + 117334002510459504 * q^98 + 83491484709877596 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\) 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				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1.18.a.a	$1$	$18$	1.a	1.a	$1$	$1$	$1$	$1.832$	\(\Q\)	None	✓	✓	✓	✓	1.18.a.a	$1$	$1$	\(-528\)	\(-4284\)	\(-1025850\)	\(3225992\)	$+$	$1$	$\mathrm{SU}(2)$	\(q-528q^{2}-4284q^{3}+147712q^{4}+\cdots\)