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Properties

Label 4.37
Level 4
Weight 37
Dimension 17
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 37
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 37 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(37\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{37}(\Gamma_1(4))\).

Total New Old
Modular forms 19 19 0
Cusp forms 17 17 0
Eisenstein series 2 2 0

Trace form

\( 17 q - 84916 q^{2} + 63108769040 q^{4} + 1587598983826 q^{5} - 217628996575488 q^{6} - 6116838281275456 q^{8} - 785089825520546847 q^{9} + O(q^{10}) \) \( 17 q - 84916 q^{2} + 63108769040 q^{4} + 1587598983826 q^{5} - 217628996575488 q^{6} - 6116838281275456 q^{8} - 785089825520546847 q^{9} - 1269669491125656104 q^{10} - 42882825786868930560 q^{12} + 41676149406206500018 q^{13} + 360192888461659120128 q^{14} - 18131657039655345618688 q^{16} + 18678125271466757001058 q^{17} + 98858065961248026757644 q^{18} - 185987631386800333033184 q^{20} - 175281296641396774711296 q^{21} - 4320007363229839528400640 q^{22} + 5118364442017682383085568 q^{24} + 64389827691705544439075331 q^{25} - 30067267580294149817323688 q^{26} - 303534200373547502486016000 q^{28} + 83558829778969622281411570 q^{29} + 361206724962468787334008320 q^{30} + 3424487663300783641955892224 q^{32} - 877278707167997370072668160 q^{33} - 2956121337393437394265165928 q^{34} + 9386969606899626916903182864 q^{36} + 1028936832542213926690666258 q^{37} + 78752216997100984306444174080 q^{38} - 61948625233183002270749961344 q^{40} + 241910655498966263829819397954 q^{41} - 193406458925326074258433843200 q^{42} + 303084904999663560614745692160 q^{44} + 876750889440806776372165555506 q^{45} - 919681205391808405630032112128 q^{46} - 1511312501851283767715389931520 q^{48} - 8690584837344731555055515727247 q^{49} + 10185343958170807211600579472036 q^{50} + 5584769803431310739681792135968 q^{52} + 2864977575306763415468638557778 q^{53} - 42689634574575573966970327785984 q^{54} - 18346492780981997297263940026368 q^{56} - 17591710635767034592583231047680 q^{57} - 13872941779387924373159026137512 q^{58} - 69704584574466315130190074982400 q^{60} + 488044483791787508231294360980594 q^{61} + 406820870675021165265665434183680 q^{62} + 58407051193644631965991706562560 q^{64} - 1419136027205678294994787009303228 q^{65} - 816784109200805225218136599695360 q^{66} + 1913850173378374444103604070923808 q^{68} + 3923547517779842564469076002041856 q^{69} + 312094823977274793710809307489280 q^{70} - 4579322712415668078348091815468096 q^{72} - 7016735948804628395640934715523902 q^{73} - 670997304617426449840386839200808 q^{74} - 15736875982808342938482824299100160 q^{76} + 22639774155764461736245527294259200 q^{77} - 18389491597233550087389536189698560 q^{78} + 47267506511318977155908021422813696 q^{80} - 18188477562036937666899669720078159 q^{81} + 5807936682837544119287618687716888 q^{82} - 37119022564017857733030089777086464 q^{84} - 109102745881421109039130518648221788 q^{85} + 102108696026625816655543232864792832 q^{86} + 39749581676781586144951142033940480 q^{88} + 536580108278993677338741367468283650 q^{89} - 195283296567279720904119484240636584 q^{90} - 17511543929609412714530045318983680 q^{92} - 231978818535002459544922699145134080 q^{93} - 696830931593880576023589572144120832 q^{94} + 1050073689946737522972596709346639872 q^{96} - 467501081650930946766716978739129182 q^{97} + 340279939831197597514188700404039884 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{37}^{\mathrm{new}}(\Gamma_1(4))\)

We only show spaces with odd 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
4.37.b \(\chi_{4}(3, \cdot)\) 4.37.b.a 1 1
4.37.b.b 16