Properties

Label 16.44
Level 16
Weight 44
Dimension 191
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 704
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 44 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(704\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{44}(\Gamma_1(16))\).

Total New Old
Modular forms 351 196 155
Cusp forms 337 191 146
Eisenstein series 14 5 9

Trace form

\( 191 q - 2 q^{2} + 10460353202 q^{3} - 4414215286264 q^{4} - 247839723078604 q^{5} + 112071446787942544 q^{6} + 574012688698122568 q^{7} - 11854171714180233644 q^{8} + 2294703116712725897017 q^{9} + O(q^{10}) \) \( 191 q - 2 q^{2} + 10460353202 q^{3} - 4414215286264 q^{4} - 247839723078604 q^{5} + 112071446787942544 q^{6} + 574012688698122568 q^{7} - 11854171714180233644 q^{8} + 2294703116712725897017 q^{9} + 5459045991232881005292 q^{10} + 72533668787005645674638 q^{11} + 771234797952038615980900 q^{12} + 67163635004959946919020 q^{13} + 9322260446532065845778876 q^{14} - 57793490933231314765855332 q^{15} + 163273800835251326368550680 q^{16} + 146956632481344296588383894 q^{17} - 1332101553634441255393276386 q^{18} + 6325297617733431800890611882 q^{19} + 35662180000530134158000592444 q^{20} + 23933060712968602086002199316 q^{21} + 69135527535366019020621277252 q^{22} + 125503031568915062237445575768 q^{23} + 138945174459992315613693126832 q^{24} + 4754864683505577347800073308979 q^{25} - 14291932291718934005921476629624 q^{26} + 13181053303852701777551172973568 q^{27} + 47590691418035655121423431268120 q^{28} - 28511315316451093299981962443948 q^{29} - 21383945736157280990547561298764 q^{30} + 128902811634707902555562045486480 q^{31} + 339193027455420108887954468928968 q^{32} - 18236389543166765548964466053780 q^{33} - 633425089825657775599108147277964 q^{34} + 2410162521696425463352701483810764 q^{35} + 17561316565193236115741687250606508 q^{36} + 901341002535456270542240434881484 q^{37} + 7243847085410196824459845300026208 q^{38} + 1242595196486749258828752926618104 q^{39} + 115004204880974614323554539333560264 q^{40} - 27537388469721603787249063387108350 q^{41} + 358432362654443961889162440629287480 q^{42} - 425350959025584067594151554036311850 q^{43} - 440824103222946660616740705654106268 q^{44} - 147370312841611452510268132304900304 q^{45} - 2030300481066349318181373531471404564 q^{46} - 2806547403993725226760620822828085376 q^{47} - 4181143536383502776551034704082732312 q^{48} - 42102189950952680781418551133716582629 q^{49} - 4261240751758384910675733061135130874 q^{50} - 4801860039488021761152797916494481460 q^{51} + 28447048937269288576922109728519951636 q^{52} + 1750438342849304869717510036298967244 q^{53} - 30639104288371161082116085153656941024 q^{54} - 45502878383834381537260230919631358968 q^{55} - 76698172755688529394576003292884482024 q^{56} - 50961546332087572780430328802554902384 q^{57} - 407226933880931094405038856007411700968 q^{58} - 114194000101110213765785306151819433898 q^{59} + 460799267099996720046639986693013338688 q^{60} + 580513239962131141465465388431545255244 q^{61} - 2174726387765026008508883255035359423440 q^{62} + 1906917723366228067875151877169091601964 q^{63} - 5052657277588898044450027146576221310976 q^{64} + 1181034814111996617860753767514793392824 q^{65} - 9977725108910525107850661722683034278508 q^{66} + 235810590568123614148970501654353267466 q^{67} + 7663467699112341296092850006197301215376 q^{68} - 13924570957067478575217186468615894419484 q^{69} + 45154466295975637431261336978411684718720 q^{70} - 10076695683951487928111801309338528958072 q^{71} + 81305595036228332111642161344640278772932 q^{72} - 2261182586895691825123262561746113505310 q^{73} + 6746909536396949399746337581815649967980 q^{74} + 127448733942921052614895928201006814547362 q^{75} - 43015162826166130145223911268639460143052 q^{76} - 20221842379110219686227769659490346270700 q^{77} + 84340436621446222217954349743385249591548 q^{78} - 348187290524113446763858843076542281945584 q^{79} + 50796688052708181159207290671842983413672 q^{80} - 1683680874148362638496548659250570356671105 q^{81} - 172418271027830711700282569383452871927232 q^{82} + 998301964317262059359862144973934202521986 q^{83} + 234851954189439372854696172417430610454184 q^{84} - 468948387570343984673956356102133426532032 q^{85} - 619778474518267049022368283346537271065276 q^{86} - 2539164505078667050139175561238708549576776 q^{87} - 663071975155965105339513899481703420327432 q^{88} + 738224977017457814875891683243731254309458 q^{89} - 2488191805753808449363415332163081913701544 q^{90} + 4406429970627100576605526760035393489646644 q^{91} + 8223506524737211884415072134677231610225272 q^{92} - 43681101238663263612849544384577729645200 q^{93} + 7539501485830147270858632334763754515415760 q^{94} + 9260214510023315464561464192793788647804908 q^{95} + 26978876590890752741622629403049129245470384 q^{96} - 1614821177658843986354696599008519836404282 q^{97} + 19161815326754362048059085131399547725511226 q^{98} + 20269811970403272820332156382938397482896842 q^{99} + O(q^{100}) \)

Decomposition of \(S_{44}^{\mathrm{new}}(\Gamma_1(16))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
16.44.a \(\chi_{16}(1, \cdot)\) 16.44.a.a 2 1
16.44.a.b 2
16.44.a.c 3
16.44.a.d 3
16.44.a.e 5
16.44.a.f 6
16.44.b \(\chi_{16}(9, \cdot)\) None 0 1
16.44.e \(\chi_{16}(5, \cdot)\) 16.44.e.a 170 2

Decomposition of \(S_{44}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{44}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{44}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{44}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)