Space of modular forms of level 9 and weight 18

• Label: 9.18
• Level: 9
• Weight: 18
• Dimension: 38
• Nonzero newspaces: 2
• Newform subspaces: 5
• Sturm bound: 108
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	55	43	12
Cusp forms	47	38	9
Eisenstein series	8	5	3

Trace form

38 * q - 15 * q^2 - 2280 * q^3 - 748333 * q^4 + 1062222 * q^5 - 11973897 * q^6 + 611620 * q^7 - 295342230 * q^8 + 361418022 * q^9 - 374218896 * q^10 + 1371243864 * q^11 - 1042595580 * q^12 - 1280823530 * q^13 + 11199259320 * q^14 - 16381898892 * q^15 - 51748987633 * q^16 + 90757602540 * q^17 - 14265083340 * q^18 - 79351147112 * q^19 + 531887211780 * q^20 + 4513668870 * q^21 - 561358869945 * q^22 + 720131131860 * q^23 - 637780167243 * q^24 - 1925876297488 * q^25 - 3714373520364 * q^26 + 5221852219080 * q^27 + 3024871191580 * q^28 + 2388312161418 * q^29 - 1660912047576 * q^30 + 7579518178612 * q^31 - 21325508925345 * q^32 + 50033782978920 * q^33 - 2585450055339 * q^34 - 81590433908784 * q^35 - 17395629139341 * q^36 + 8437181179900 * q^37 + 33808164727155 * q^38 - 136585826031300 * q^39 - 38456447095968 * q^40 + 223615414083012 * q^41 + 519138286202610 * q^42 + 6020237735080 * q^43 - 719269610931798 * q^44 - 207448243757802 * q^45 + 297570527351304 * q^46 + 847601821046820 * q^47 - 1459321192573725 * q^48 - 785257011086148 * q^49 + 1409761710225489 * q^50 + 1557462134297520 * q^51 - 318470850277430 * q^52 - 1208663148203640 * q^53 - 800270910205191 * q^54 + 1183676178457176 * q^55 + 889003547973390 * q^56 - 2222650708198350 * q^57 - 713340177675180 * q^58 + 1155307123059936 * q^59 + 2526793245608868 * q^60 + 3431103514040194 * q^61 - 13321504218812700 * q^62 + 2697071243839020 * q^63 + 3230363715539906 * q^64 - 2083574250649914 * q^65 + 10217290425379578 * q^66 + 1157538076856680 * q^67 - 10293536967373665 * q^68 + 385548989756562 * q^69 - 2927617208897694 * q^70 + 37109771013305808 * q^71 - 7500347776120005 * q^72 - 30909346344502880 * q^73 - 37901977414206708 * q^74 + 45866526570711528 * q^75 + 16587980028291517 * q^76 + 9777200274591630 * q^77 - 93683140186739850 * q^78 - 28985283932197916 * q^79 + 58380670691371968 * q^80 + 41504778032702238 * q^81 + 39014900714819670 * q^82 + 24278148822794160 * q^83 + 97689016707023442 * q^84 - 8440591676464332 * q^85 - 154976504013381423 * q^86 - 56007566311800060 * q^87 + 26640704623517835 * q^88 + 121718685949455240 * q^89 - 181676628175391892 * q^90 + 125386537548165680 * q^91 - 213666047253854670 * q^92 - 12154449845289750 * q^93 - 84255661960127376 * q^94 + 241683438164699424 * q^95 + 167081640420235104 * q^96 + 82722805346577760 * q^97 - 558480970739017440 * q^98 - 150580077529929192 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
9.18.a	\(\chi_{9}(1, \cdot)\)	9.18.a.a	1	1
		9.18.a.b	1
		9.18.a.c	2
		9.18.a.d	2
9.18.c	\(\chi_{9}(4, \cdot)\)	9.18.c.a	32	2

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)