Space of modular forms of level 9 and weight 16

• Label: 9.16
• Level: 9
• Weight: 16
• Dimension: 34
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 96
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 9 = 3^{2} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(9))\).

	Total	New	Old
Modular forms	49	39	10
Cusp forms	41	34	7
Eisenstein series	8	5	3

Trace form

34 * q - 39 * q^2 + 3345 * q^3 - 63245 * q^4 - 263985 * q^5 + 2208231 * q^6 - 3833803 * q^7 + 17372874 * q^8 - 15596991 * q^9 + 72831072 * q^10 - 152523210 * q^11 + 182013108 * q^12 + 114413435 * q^13 - 870427968 * q^14 - 657143253 * q^15 + 3385752463 * q^16 - 7519760568 * q^17 + 7761499596 * q^18 + 5812908530 * q^19 - 14439690348 * q^20 + 18429715101 * q^21 + 27811138119 * q^22 - 51701220105 * q^23 - 22375042227 * q^24 - 60694221269 * q^25 + 138847810548 * q^26 + 162819945072 * q^27 - 527169172036 * q^28 + 48605645553 * q^29 + 588495022128 * q^30 + 242767446425 * q^31 - 663826164273 * q^32 - 752623919694 * q^33 - 81694659915 * q^34 + 2566441619286 * q^35 - 98909775117 * q^36 - 210563897152 * q^37 - 4857394070589 * q^38 + 3663944150079 * q^39 + 4495804779336 * q^40 - 4527337851078 * q^41 - 12459707404686 * q^42 + 6169386285512 * q^43 + 13176755222442 * q^44 + 4884357020085 * q^45 - 12187591387224 * q^46 - 7872218416407 * q^47 + 12130882824291 * q^48 - 6982268524389 * q^49 + 16460748817809 * q^50 + 5493352002093 * q^51 - 11111574488686 * q^52 - 18173629905030 * q^53 - 8013203434503 * q^54 - 7167647851026 * q^55 + 38102520844014 * q^56 - 15469760310585 * q^57 - 51684278201148 * q^58 - 23213211747054 * q^59 + 143327945409084 * q^60 + 40734510082397 * q^61 - 179472703471260 * q^62 + 41573408563611 * q^63 + 181674971889154 * q^64 - 67735045720065 * q^65 - 193311009227574 * q^66 - 18111432891340 * q^67 + 124952944189959 * q^68 + 270237544770987 * q^69 - 286550354936478 * q^70 + 10065140778312 * q^71 - 121608306427509 * q^72 + 436048220789546 * q^73 + 51576894410772 * q^74 - 327902975378103 * q^75 - 601696651619587 * q^76 - 53002926936123 * q^77 - 527565898825578 * q^78 + 455664581709407 * q^79 + 1758334990883232 * q^80 + 316134370401669 * q^81 - 668253144271578 * q^82 - 397311068428185 * q^83 - 262197855811446 * q^84 + 189823062933666 * q^85 - 1338536820409215 * q^86 - 1151998177977873 * q^87 + 1593209504920971 * q^88 + 2940672425509386 * q^89 + 1343761639138764 * q^90 - 1487743938333794 * q^91 - 4337086416010494 * q^92 + 309143584649451 * q^93 + 2511258072054792 * q^94 - 3789939941878188 * q^95 - 236708398351224 * q^96 - 2124018146111644 * q^97 + 5880039188509368 * q^98 + 5495206589055945 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)

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
9.16.a	\(\chi_{9}(1, \cdot)\)	9.16.a.a	1	1
		9.16.a.b	1
		9.16.a.c	1
		9.16.a.d	1
		9.16.a.e	2
9.16.c	\(\chi_{9}(4, \cdot)\)	9.16.c.a	28	2

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(9))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(9)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)