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Properties

Label 18.40
Level 18
Weight 40
Dimension 94
Nonzero newspaces 2
Newform subspaces 10
Sturm bound 720
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 40 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 10 \)
Sturm bound: \(720\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{40}(\Gamma_1(18))\).

Total New Old
Modular forms 359 94 265
Cusp forms 343 94 249
Eisenstein series 16 0 16

Trace form

\( 94 q + 524288 q^{2} + 1610301495 q^{3} - 6322191859712 q^{4} + 66372440325462 q^{5} + 3008511327338496 q^{6} - 30487592739046636 q^{7} - 288230376151711744 q^{8} - 9408179818166261181 q^{9} + O(q^{10}) \) \( 94 q + 524288 q^{2} + 1610301495 q^{3} - 6322191859712 q^{4} + 66372440325462 q^{5} + 3008511327338496 q^{6} - 30487592739046636 q^{7} - 288230376151711744 q^{8} - 9408179818166261181 q^{9} - 15568957438030774272 q^{10} + 21329595130783135179 q^{11} - 59222757862142902272 q^{12} + 3676566746550564090368 q^{13} + 55329905666261118877696 q^{14} - 136085393361812587021350 q^{15} - 1737830865696029438640128 q^{16} - 2820946075473475071471498 q^{17} + 2885111312329532091924480 q^{18} - 10967627269445353408515214 q^{19} + 18244317475428536709808128 q^{20} - 37510883982687100142589804 q^{21} - 112800123201092997490409472 q^{22} - 948820820580431033069156808 q^{23} - 20087482663701431967547392 q^{24} - 9286608683156043660866925143 q^{25} + 7796737828046823668051869696 q^{26} + 13667379096969036075174190128 q^{27} - 16519009025316895674754662400 q^{28} + 157103582813889240309442893840 q^{29} + 204825342726961686996804698112 q^{30} - 73563418979214311499181708942 q^{31} + 39614081257132168796771975168 q^{32} - 2501474321904800984065515134367 q^{33} + 1143778569233376228588397264896 q^{34} - 3239660970168965406101121195132 q^{35} + 1703937078617249627665801936896 q^{36} - 8998438615639295838139731075328 q^{37} + 2633886039048764863876017160192 q^{38} + 8301418635486892157244857105202 q^{39} - 4279562433866119816947085344768 q^{40} + 160449406731083282757680331280737 q^{41} - 74150876342475618082817430257664 q^{42} + 114028808960085679710314143939709 q^{43} + 215925011563846980767259379630080 q^{44} + 226545778184483621167790610689658 q^{45} + 502765484569186648693809233264640 q^{46} - 1289492739622168638390147971951868 q^{47} - 105391913192248944172595310231552 q^{48} - 4086189025249745700841702456728573 q^{49} + 387137786706720162854875633811456 q^{50} - 168579029430585431653031270643141 q^{51} + 1010606972031730789022883110715392 q^{52} - 12710591768980084000390827793972716 q^{53} + 22872460887847725813349788103999488 q^{54} - 33002568676313297205485914628172252 q^{55} + 15208968660950822155268642805121024 q^{56} + 45486729294532012805920382627144223 q^{57} - 9190160938658895112544117534490624 q^{58} + 93178384233708297147275694878208357 q^{59} - 43412924381924216494339947837259776 q^{60} + 154756936550355179083370522381947850 q^{61} - 551313498453410579018520645664243712 q^{62} + 598881911992773082592437353107347422 q^{63} + 1952303618809095188327466619786756096 q^{64} - 55957470369089311566201850820545914 q^{65} + 1450205488705597915693544951123017728 q^{66} + 644438034729747867727885570558698959 q^{67} + 220660700475260363630882259015303168 q^{68} + 914113582701501990481137960942803094 q^{69} - 2064737319235560183558850709764964352 q^{70} + 12538974743668091802177822102761078616 q^{71} - 2853137021297438165479000235525013504 q^{72} + 7446418070099158027377480463851497966 q^{73} + 5013784187539113638199261445601886208 q^{74} - 18890121619710119731643143233643954989 q^{75} + 2864608208504436925764102391127343104 q^{76} - 7526080307398402351483431435548939244 q^{77} - 17714221883597245270041377189233950720 q^{78} + 9847109854229149752383178377288774486 q^{79} - 14357707016368984567366225753257541632 q^{80} + 32508885368001262435973600128213983759 q^{81} - 3083932172991705055222331550232215552 q^{82} + 123012928719200464023125475064056448302 q^{83} + 5788940501059523818106715318018637824 q^{84} - 115173209444160650222505097549376282268 q^{85} + 185113535684542342241483531140091871232 q^{86} + 48782730803294730769498093744842945588 q^{87} - 31006261768541776363258800376872173568 q^{88} - 287851844470392721336168544769487809456 q^{89} + 294077280500204495506419140083631259648 q^{90} - 879177871874152446223932206917357598084 q^{91} - 260809881226037441575393471785968074752 q^{92} + 450350804967564028840760141411769328134 q^{93} - 828595717814470735681307235455289262080 q^{94} + 2956050063387868939746048586750734772344 q^{95} - 221795083698539564614804080527469969408 q^{96} - 809196837104797299929196929204633166535 q^{97} + 1558859990156082822394907930896182018048 q^{98} - 815046184261447906329043752010553487792 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{40}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.40.a \(\chi_{18}(1, \cdot)\) 18.40.a.a 1 1
18.40.a.b 1
18.40.a.c 2
18.40.a.d 2
18.40.a.e 2
18.40.a.f 2
18.40.a.g 3
18.40.a.h 3
18.40.c \(\chi_{18}(7, \cdot)\) 18.40.c.a 38 2
18.40.c.b 40

Decomposition of \(S_{40}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{40}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{40}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{40}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{40}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{40}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{40}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)