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Properties

Label 36.5
Level 36
Weight 5
Dimension 63
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 360
Trace bound 1

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(360\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(36))\).

Total New Old
Modular forms 164 73 91
Cusp forms 124 63 61
Eisenstein series 40 10 30

Trace form

\( 63 q - 3 q^{2} - 9 q^{3} - 13 q^{4} - 21 q^{5} + 15 q^{6} + 149 q^{7} + 186 q^{8} - 39 q^{9} + O(q^{10}) \) \( 63 q - 3 q^{2} - 9 q^{3} - 13 q^{4} - 21 q^{5} + 15 q^{6} + 149 q^{7} + 186 q^{8} - 39 q^{9} + 136 q^{10} - 18 q^{11} - 228 q^{12} + 75 q^{13} - 348 q^{14} + 225 q^{15} - 625 q^{16} + 222 q^{17} + 72 q^{18} + 146 q^{19} + 1452 q^{20} - 1029 q^{21} + 1143 q^{22} - 1719 q^{23} - 951 q^{24} - 3230 q^{25} - 1548 q^{26} + 648 q^{27} - 3060 q^{28} + 1671 q^{29} - 1980 q^{30} + 3491 q^{31} + 3687 q^{32} + 6252 q^{33} + 3541 q^{34} - 1005 q^{36} - 234 q^{37} - 3285 q^{38} - 8265 q^{39} - 4196 q^{40} - 8196 q^{41} + 3330 q^{42} + 2252 q^{43} + 10410 q^{44} + 9789 q^{45} + 7800 q^{46} + 13689 q^{47} + 2163 q^{48} + 2852 q^{49} + 5697 q^{50} + 10449 q^{51} + 3526 q^{52} - 17682 q^{53} - 4983 q^{54} - 13482 q^{55} - 9234 q^{56} - 20109 q^{57} - 11012 q^{58} - 20052 q^{59} - 16392 q^{60} + 3 q^{61} - 11100 q^{62} + 5559 q^{63} + 4418 q^{64} + 38811 q^{65} - 17358 q^{66} + 12938 q^{67} - 22053 q^{68} + 24999 q^{69} - 6366 q^{70} + 4083 q^{72} - 30864 q^{73} + 27384 q^{74} - 30297 q^{75} + 23901 q^{76} - 50511 q^{77} + 34566 q^{78} - 16315 q^{79} + 23472 q^{80} + 18537 q^{81} - 6482 q^{82} + 37017 q^{83} + 51078 q^{84} + 58274 q^{85} + 41673 q^{86} + 22455 q^{87} + 21003 q^{88} + 47886 q^{89} - 4692 q^{90} + 13654 q^{91} - 49110 q^{92} - 24399 q^{93} - 29964 q^{94} - 37116 q^{95} - 76164 q^{96} + 3834 q^{97} - 77484 q^{98} - 10035 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.5.c \(\chi_{36}(17, \cdot)\) 36.5.c.a 2 1
36.5.d \(\chi_{36}(19, \cdot)\) 36.5.d.a 1 1
36.5.d.b 4
36.5.d.c 4
36.5.f \(\chi_{36}(7, \cdot)\) 36.5.f.a 44 2
36.5.g \(\chi_{36}(5, \cdot)\) 36.5.g.a 8 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 1}\)