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Properties

Label 16.36
Level 16
Weight 36
Dimension 155
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 576
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 36 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(576\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_1(16))\).

Total New Old
Modular forms 287 160 127
Cusp forms 273 155 118
Eisenstein series 14 5 9

Trace form

\( 155 q - 2 q^{2} + 129140162 q^{3} + 8427741320 q^{4} + 740368852316 q^{5} - 63531047368688 q^{6} - 124747377106072 q^{7} - 13699480913441324 q^{8} + 239150871423581125 q^{9} + O(q^{10}) \) \( 155 q - 2 q^{2} + 129140162 q^{3} + 8427741320 q^{4} + 740368852316 q^{5} - 63531047368688 q^{6} - 124747377106072 q^{7} - 13699480913441324 q^{8} + 239150871423581125 q^{9} + 562006145471489132 q^{10} + 4510701111741908606 q^{11} - 479089310900991260 q^{12} + 15396219882905618420 q^{13} + 8799826775229311036 q^{14} - 301916623514264043012 q^{15} - 3190079279323819640552 q^{16} + 1777574123744166436174 q^{17} + 50291204415702930751134 q^{18} + 30717287591711139963514 q^{19} - 203685070951610175281476 q^{20} - 18936889424714712352556 q^{21} + 636966940831716653885252 q^{22} - 652274208658450247906632 q^{23} - 2487231207332545389918032 q^{24} + 6388569973708720950712439 q^{25} + 17773534465890877728972168 q^{26} + 28768989426907208607686048 q^{27} - 30502914202561178874504680 q^{28} - 6262148526068764532810788 q^{29} - 285612926517420648109378764 q^{30} + 514517024567044116241164304 q^{31} - 738658719158089208252773432 q^{32} - 349119761365195910265768020 q^{33} - 42049737777132205084612492 q^{34} + 3017735856358826136173741324 q^{35} - 5164214322025715072062402388 q^{36} - 3492850053852713635657141836 q^{37} - 9801087374101452610071505952 q^{38} - 1617462869452776393075599144 q^{39} + 8026342558748957174517830344 q^{40} - 4484029239970739096676029478 q^{41} + 6782379290655229156691711800 q^{42} - 20897724320911085051204033850 q^{43} - 42659032050426125747024157212 q^{44} + 92010664048268703388162384056 q^{45} - 832824703575483585919309676180 q^{46} - 266785500082455314889732598976 q^{47} - 2394587002270018938900110805272 q^{48} - 5479577134763701260267754700713 q^{49} - 2745109752376550429343334199034 q^{50} + 2231313921245039070649074560108 q^{51} + 2593888727625933053060676205716 q^{52} + 369112304822752194918768330484 q^{53} + 3720773498739838314153063297568 q^{54} - 8008551899283503132352242860248 q^{55} - 7032341759990636102318643474920 q^{56} + 4599404071149575145263912493136 q^{57} - 14920763784011367012582015273448 q^{58} - 27030177421293154452691117721978 q^{59} + 8127032555398081539102017663808 q^{60} - 24987398092384350263311001428332 q^{61} + 150862788237632040277846643356720 q^{62} - 37690448059832614326907459445556 q^{63} + 81200319701242603746760832145920 q^{64} - 20152395692561793965139223689176 q^{65} + 186161394336520764059070324142612 q^{66} + 194217695522595369499860319017626 q^{67} - 383667797451609978651798061558384 q^{68} + 623878940460523957833486343359012 q^{69} - 49174652206146817082980223392640 q^{70} - 929005073620983827751407316730712 q^{71} - 435073443598655211850464003815868 q^{72} + 376495792983246083951662468292410 q^{73} - 1950041943640302246884367595097876 q^{74} - 368216910738509474069338492485678 q^{75} + 2132028376780474170909842207973812 q^{76} + 913355588327968038745535865723860 q^{77} - 7058266191082442347583246700509572 q^{78} - 1746261519089026822211054711865264 q^{79} - 11335810123270027244913467056407128 q^{80} - 31133262052215322389330931483352133 q^{81} + 8452152820217551578367859539645888 q^{82} + 10431834313433275768715206713093586 q^{83} - 33640033066196884498564669457317208 q^{84} + 3174534272388886023140429631867728 q^{85} + 35773596881339666417542325019717188 q^{86} + 25592466244391696066657502430066584 q^{87} + 34889463603669368774761399210820088 q^{88} + 8613176478348894710226227694339690 q^{89} - 171873606334321612116861586473075624 q^{90} - 46866087323337205874994906220329996 q^{91} + 204534370870358263053212149856805752 q^{92} + 2523720463876173553225786873982960 q^{93} + 72825251469755242539931383675378640 q^{94} + 268682989471349130025372517448581068 q^{95} + 27525214015686889713168652157185712 q^{96} - 99144796361353766381381839617526722 q^{97} + 504064541858763530197734120399518906 q^{98} + 422733231366363510907661270966208442 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.36.a \(\chi_{16}(1, \cdot)\) 16.36.a.a 1 1
16.36.a.b 1
16.36.a.c 3
16.36.a.d 3
16.36.a.e 4
16.36.a.f 5
16.36.b \(\chi_{16}(9, \cdot)\) None 0 1
16.36.e \(\chi_{16}(5, \cdot)\) 16.36.e.a 138 2

Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{36}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)