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Properties

Label 16.34
Level 16
Weight 34
Dimension 146
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 544
Trace bound 1

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Defining parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 34 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(544\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_1(16))\).

Total New Old
Modular forms 271 151 120
Cusp forms 257 146 111
Eisenstein series 14 5 9

Trace form

\( 146 q - 2 q^{2} - 43046722 q^{3} - 12450833112 q^{4} - 156622672802 q^{5} + 15169141501168 q^{6} + 134757061640576 q^{7} + 1567628306374324 q^{8} + 28649461854806224 q^{9} + O(q^{10}) \) \( 146 q - 2 q^{2} - 43046722 q^{3} - 12450833112 q^{4} - 156622672802 q^{5} + 15169141501168 q^{6} + 134757061640576 q^{7} + 1567628306374324 q^{8} + 28649461854806224 q^{9} - 71874512917548596 q^{10} - 416956012713406654 q^{11} + 1137959622509533636 q^{12} + 631640266927430878 q^{13} - 2353646973005552932 q^{14} + 38638433032955231364 q^{15} - 24274157474973943400 q^{16} - 14750840754426906340 q^{17} - 1589720662155750799938 q^{18} - 5913785808943844544058 q^{19} - 1927099131179326848548 q^{20} + 3283578106411408320772 q^{21} - 1340925075432209755900 q^{22} + 30132309299292237300864 q^{23} - 355295947512959431094096 q^{24} + 436051148161122927589872 q^{25} - 483589603755353944141304 q^{26} - 215785684598624407778440 q^{27} - 190392305051346627155752 q^{28} + 1965041800414795107374310 q^{29} + 9173877995294428636206036 q^{30} - 11137372983966310074950160 q^{31} + 6180821631393580822651208 q^{32} - 4213962601967366318650628 q^{33} - 42111929978265704422540108 q^{34} - 75560939559231446191843588 q^{35} - 153918593775904625819415956 q^{36} + 27544211885427388787337574 q^{37} - 231988417600624985864186112 q^{38} + 38669905700002881199000192 q^{39} - 1800891970531134889476784248 q^{40} + 276821689532571107877716640 q^{41} - 621980378620861230777297800 q^{42} - 2116152318060047003713251510 q^{43} + 2712484225219333284846178436 q^{44} - 2924040783382089257442515742 q^{45} + 11220213143077049503107298380 q^{46} + 22689857106089050411127401744 q^{47} + 14798478573676754485112814568 q^{48} - 115560782007479857912474017514 q^{49} - 37548902406186710568437990010 q^{50} - 100732472405365361452892350588 q^{51} + 103567457457944545545469811572 q^{52} - 62493243678638224368290853802 q^{53} + 113151258575497624391289169696 q^{54} + 106472340450821333332621315456 q^{55} + 255584218119246648637737690520 q^{56} - 68762594313718174825608299264 q^{57} - 31727385056134370176506024744 q^{58} - 330076632508574358678831334854 q^{59} - 417186807889982291104029115008 q^{60} + 408971153272335788558427763150 q^{61} + 548656301949952603150780023856 q^{62} + 575054847093282056466280486788 q^{63} + 1642957543860290177269369575552 q^{64} + 386059856981289315067429647940 q^{65} - 5134572565890671104827875033036 q^{66} - 2012775753997081053570930755914 q^{67} + 5705065546067589840320699654352 q^{68} - 7920277694757618807251337685260 q^{69} - 6859721260148110165774159020160 q^{70} - 6165658024321985591365473727104 q^{71} - 19956189830433674977588304763996 q^{72} - 484969593988414398422159930208 q^{73} + 34719513730216198307919903799884 q^{74} + 2991361636236114417274461567558 q^{75} - 51013558490802024872088197550828 q^{76} - 8481260413218820983556901883644 q^{77} + 79364965335834772336303980975836 q^{78} - 40157558770218065554557667026176 q^{79} + 110877540658623100118409496501544 q^{80} - 301467100767787329634002593934054 q^{81} - 263535572750697474563853467785824 q^{82} + 94298675878227641697186965358526 q^{83} + 607831672096349837517067994605480 q^{84} - 12048045630438218948192098133564 q^{85} + 399643619821153405551443261010564 q^{86} - 171352102230431304073787049830784 q^{87} + 306400215215978432497278268141048 q^{88} - 253519755321907827102752545313376 q^{89} + 1561513640555280385360731386337432 q^{90} - 958765943397284544952145235833596 q^{91} - 851574763037555457083199819351624 q^{92} - 311009233270720128164096062839280 q^{93} + 1550904319846519657005686020088336 q^{94} + 1733393504252750700046039884760692 q^{95} + 3869279984472308526612664725668528 q^{96} - 161151355299924386861891787981284 q^{97} - 18273313838066356258319804470182 q^{98} - 6748016895296303902062157074441410 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.34.a \(\chi_{16}(1, \cdot)\) 16.34.a.a 1 1
16.34.a.b 2
16.34.a.c 2
16.34.a.d 3
16.34.a.e 4
16.34.a.f 4
16.34.b \(\chi_{16}(9, \cdot)\) None 0 1
16.34.e \(\chi_{16}(5, \cdot)\) 16.34.e.a 130 2

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{34}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)