Space of modular forms of level 16 and weight 18

• Label: 16.18
• Level: 16
• Weight: 18
• Dimension: 74
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 288
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 16 = 2^{4} \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(16))\).

	Total	New	Old
Modular forms	143	79	64
Cusp forms	129	74	55
Eisenstein series	14	5	9

Trace form

74 * q - 2 * q^2 - 6562 * q^3 - 54744 * q^4 - 12242 * q^5 - 9659408 * q^6 + 13155520 * q^7 - 101532236 * q^8 + 381202024 * q^9 + 284165324 * q^10 - 629746270 * q^11 + 647301316 * q^12 - 795138962 * q^13 + 6580735964 * q^14 + 43357282884 * q^15 + 49260326296 * q^16 + 9464779916 * q^17 - 154774440258 * q^18 - 160260341018 * q^19 + 534629724892 * q^20 - 127977749372 * q^21 + 344069189380 * q^22 - 169801828800 * q^23 - 1845764583248 * q^24 + 327793560312 * q^25 + 3054933980680 * q^26 - 895065396808 * q^27 - 3163268182312 * q^28 - 3747885438858 * q^29 + 1112739979476 * q^30 - 12582925000976 * q^31 - 14092609233592 * q^32 - 195602811524 * q^33 + 4421458841268 * q^34 - 42636908870788 * q^35 - 78648071112596 * q^36 - 29610623095114 * q^37 + 26879344539648 * q^38 + 40546924882240 * q^39 + 78479998694792 * q^40 - 9753146876592 * q^41 - 280546585448840 * q^42 + 61410640185770 * q^43 + 353399653694852 * q^44 - 18045065496462 * q^45 - 205880797854900 * q^46 + 259006469750416 * q^47 - 336693732420632 * q^48 - 1370075944811378 * q^49 + 633347781304710 * q^50 + 507539017453508 * q^51 - 250572184348044 * q^52 - 1382682749134810 * q^53 + 1545312889650976 * q^54 + 453009721885376 * q^55 + 1727282544382360 * q^56 - 1096531773403520 * q^57 - 4743213379910952 * q^58 - 3791819174161638 * q^59 + 12475663393894272 * q^60 + 4331243185960670 * q^61 - 1023265995226064 * q^62 - 2157599059654716 * q^63 - 4803736754115456 * q^64 + 2429294956866340 * q^65 + 34592600807745844 * q^66 + 8347599866621270 * q^67 - 30604279033681200 * q^68 - 16045751573030028 * q^69 + 24438949220497280 * q^70 - 6110717387570496 * q^71 + 30860656197322404 * q^72 - 9399120337579440 * q^73 - 48718480417927860 * q^74 - 46430308023123162 * q^75 + 43334084125892628 * q^76 + 30874630657902724 * q^77 - 3562265224457764 * q^78 - 389424450361984 * q^79 + 5755873605839144 * q^80 - 82391387373730158 * q^81 + 16449314794081440 * q^82 - 129539042555089442 * q^83 + 1829809934827432 * q^84 - 47862322723929884 * q^85 - 17054234444405628 * q^86 + 57285930233352000 * q^87 + 67522006496247288 * q^88 - 17574490465707312 * q^89 + 157628356281694872 * q^90 + 92783259041889924 * q^91 - 64767112552277064 * q^92 - 35713337594727664 * q^93 + 12145263016662032 * q^94 - 355469009965492428 * q^95 + 92392677588189872 * q^96 - 71510264285450484 * q^97 + 38163698339299674 * q^98 + 164675678974086046 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.18.a	\(\chi_{16}(1, \cdot)\)	16.18.a.a	1	1
		16.18.a.b	1
		16.18.a.c	2
		16.18.a.d	2
		16.18.a.e	2
16.18.b	\(\chi_{16}(9, \cdot)\)	None	0	1
16.18.e	\(\chi_{16}(5, \cdot)\)	16.18.e.a	66	2

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 1}\)