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Properties

Label 36.17
Level 36
Weight 17
Dimension 265
Nonzero newspaces 4
Sturm bound 1224
Trace bound 1

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1224\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(36))\).

Total New Old
Modular forms 596 275 321
Cusp forms 556 265 291
Eisenstein series 40 10 30

Trace form

\( 265 q + 93 q^{2} + 5859 q^{3} + 11315 q^{4} + 330519 q^{5} - 374385 q^{6} - 8048339 q^{7} + 21788538 q^{8} + 28810653 q^{9} + O(q^{10}) \) \( 265 q + 93 q^{2} + 5859 q^{3} + 11315 q^{4} + 330519 q^{5} - 374385 q^{6} - 8048339 q^{7} + 21788538 q^{8} + 28810653 q^{9} + 273092776 q^{10} + 94256874 q^{11} - 151241988 q^{12} + 63576887 q^{13} + 402835428 q^{14} - 9324671175 q^{15} + 2677440143 q^{16} + 592689546 q^{17} - 47140321464 q^{18} + 1838759914 q^{19} + 12383507532 q^{20} - 94114754013 q^{21} - 86779788009 q^{22} + 390827530449 q^{23} - 371633210439 q^{24} - 1347719649940 q^{25} + 1282598312436 q^{26} + 603535755672 q^{27} - 829454714292 q^{28} - 1037256529173 q^{29} + 357751193940 q^{30} + 2265943271179 q^{31} - 1445142420537 q^{32} - 2122439981664 q^{33} - 356648209115 q^{34} + 2879003889939 q^{36} + 2936309367674 q^{37} - 765671330565 q^{38} - 1595942461929 q^{39} - 12516473750996 q^{40} + 29413561671420 q^{41} + 10258914401874 q^{42} + 16027043965408 q^{43} - 70350290153046 q^{44} - 55878951556011 q^{45} + 82658596451736 q^{46} + 78898493501001 q^{47} + 36276217189491 q^{48} + 111780161020034 q^{49} - 147865707904863 q^{50} + 33502192703973 q^{51} + 325882804930582 q^{52} - 122259819083190 q^{53} - 660603313894839 q^{54} + 234915603830838 q^{55} + 114062769913518 q^{56} - 67829593370601 q^{57} + 294724056336940 q^{58} + 30080119235112 q^{59} - 577997419913112 q^{60} + 1171447576306199 q^{61} - 343094636618172 q^{62} + 340239938383311 q^{63} + 254609655915458 q^{64} - 312966019136349 q^{65} + 773054295062178 q^{66} + 2591679347957662 q^{67} + 211825628145003 q^{68} - 2739112256624745 q^{69} - 401183442046446 q^{70} + 737395904076819 q^{72} + 5509592264080484 q^{73} + 2541650242462536 q^{74} - 28005623621877 q^{75} - 1699541400170019 q^{76} - 4171482871437951 q^{77} - 850618585192026 q^{78} + 6487597083375349 q^{79} + 15249617844592752 q^{80} - 4593854731034307 q^{81} + 4258005435999214 q^{82} - 5704097034480327 q^{83} - 17823280004563146 q^{84} + 16729523177898674 q^{85} + 14383085931895401 q^{86} + 3361296421005255 q^{87} + 1269926899972107 q^{88} - 12497286996372150 q^{89} - 9473981544083892 q^{90} + 6669980742513638 q^{91} - 29280423904970166 q^{92} + 24125962508920017 q^{93} + 15985756648413396 q^{94} + 8617227398318844 q^{95} + 45935066455150476 q^{96} - 4029048801852742 q^{97} - 105209264414381772 q^{98} + 14791089201638733 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.17.c \(\chi_{36}(17, \cdot)\) 36.17.c.a 6 1
36.17.d \(\chi_{36}(19, \cdot)\) 36.17.d.a 1 1
36.17.d.b 6
36.17.d.c 16
36.17.d.d 16
36.17.f \(\chi_{36}(7, \cdot)\) n/a 188 2
36.17.g \(\chi_{36}(5, \cdot)\) 36.17.g.a 32 2

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

Decomposition of \(S_{17}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{17}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{17}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 1}\)