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Properties

Label 36.27
Level 36
Weight 27
Dimension 432
Nonzero newspaces 4
Sturm bound 1944
Trace bound 1

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 27 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1944\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{27}(\Gamma_1(36))\).

Total New Old
Modular forms 956 442 514
Cusp forms 916 432 484
Eisenstein series 40 10 30

Trace form

\( 432 q + 181 q^{2} + 606603 q^{3} + 16622547 q^{4} + 287318531 q^{5} + 13112934111 q^{6} + 186163040559 q^{7} - 1349705505638 q^{8} + 3728434907001 q^{9} + O(q^{10}) \) \( 432 q + 181 q^{2} + 606603 q^{3} + 16622547 q^{4} + 287318531 q^{5} + 13112934111 q^{6} + 186163040559 q^{7} - 1349705505638 q^{8} + 3728434907001 q^{9} + 17896931446776 q^{10} + 90653582738628 q^{11} - 323142208076916 q^{12} - 57290368920213 q^{13} - 156531767533092 q^{14} - 731987097581565 q^{15} - 10562033382653169 q^{16} - 16221296952003292 q^{17} + 26213246555724912 q^{18} + 13885389444043026 q^{19} - 118871423582790916 q^{20} + 31436043204372981 q^{21} - 99533843445522345 q^{22} - 637162837273874061 q^{23} + 4555826400582609825 q^{24} - 23456977359867835143 q^{25} + 14996090416252231892 q^{26} + 678579878198944800 q^{27} + 7193440302653811372 q^{28} - 37868330535869396989 q^{29} - 50809353858044842164 q^{30} + 10478235464572227849 q^{31} - 198911742469620782249 q^{32} + 459733381998909192282 q^{33} - 59574403719429767355 q^{34} - 445035309123371170797 q^{36} - 81528758949396630360 q^{37} - 956017537075922411925 q^{38} + 1104317585772774105 q^{39} - 1164975290906949439356 q^{40} + 1031047870074286911476 q^{41} - 7525880541863975704494 q^{42} + 2033829089997255963594 q^{43} + 1720829092656333335850 q^{44} + 5820007103015110442643 q^{45} - 14875416742279164378120 q^{46} + 22982997836022710460399 q^{47} + 13151662110687141111987 q^{48} + 60087614020114561381149 q^{49} + 58709240492698766926881 q^{50} - 43178647582245215923299 q^{51} - 71205440700241724688306 q^{52} - 128753248306928247790636 q^{53} + 116524092319674468389769 q^{54} - 38673592429034239862310 q^{55} - 334040663434712485337586 q^{56} + 46099617185762777043975 q^{57} + 192863732103926197838844 q^{58} - 345134636527222936006362 q^{59} + 888424502924183805830736 q^{60} + 333609173971234171764279 q^{61} - 184111209235170841814460 q^{62} - 1366887577004032503243459 q^{63} + 1391150433833171322789378 q^{64} + 1859660600670045314790805 q^{65} - 666544493692046475065838 q^{66} - 322414325349061432632084 q^{67} + 1208745967672561894635971 q^{68} + 3983917725025158261768813 q^{69} + 1363726671949615630617810 q^{70} - 754998113309475309074109 q^{72} - 4534775847035176284181170 q^{73} - 5372446095457990792431616 q^{74} + 11410397736417699421987503 q^{75} + 6039120073801887068654109 q^{76} - 17060409186635671220932461 q^{77} + 4879703821308835885885830 q^{78} + 9703290389888842776936915 q^{79} - 47567771143285593424810480 q^{80} + 20472950917522377870962145 q^{81} - 27053256807066914468004834 q^{82} - 8909237520149782631060241 q^{83} - 29061633022477626799110594 q^{84} - 55460544825204735555537450 q^{85} + 2129456387343844868418297 q^{86} + 9804354277989997024038657 q^{87} + 37075335608671360807032075 q^{88} - 204542633711329596780527284 q^{89} - 63780638570280981141991380 q^{90} + 24390257498644343283836466 q^{91} - 70916571807630533605781766 q^{92} - 340180052801989640730110565 q^{93} - 35423504292271388385860292 q^{94} + 255068070325019239385903616 q^{95} + 240700202135196560337861540 q^{96} - 111675476670357381670183554 q^{97} - 501970493340112404102296996 q^{98} + 250058534229571267744262955 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{27}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.27.c \(\chi_{36}(17, \cdot)\) 36.27.c.a 8 1
36.27.d \(\chi_{36}(19, \cdot)\) 36.27.d.a 1 1
36.27.d.b 1
36.27.d.c 12
36.27.d.d 24
36.27.d.e 26
36.27.f \(\chi_{36}(7, \cdot)\) n/a 308 2
36.27.g \(\chi_{36}(5, \cdot)\) 36.27.g.a 52 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{27}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{27}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{27}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{27}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 1}\)