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Properties

Label 36.8
Level 36
Weight 8
Dimension 111
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 576
Trace bound 4

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(576\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(36))\).

Total New Old
Modular forms 272 119 153
Cusp forms 232 111 121
Eisenstein series 40 8 32

Trace form

\( 111 q - 3 q^{2} - 53 q^{4} + 423 q^{5} + 213 q^{6} - 311 q^{7} - 858 q^{9} + O(q^{10}) \) \( 111 q - 3 q^{2} - 53 q^{4} + 423 q^{5} + 213 q^{6} - 311 q^{7} - 858 q^{9} + 2648 q^{10} + 8097 q^{11} - 18822 q^{12} - 13227 q^{13} + 43482 q^{14} - 7875 q^{15} - 3065 q^{16} + 58764 q^{17} - 72144 q^{18} - 1760 q^{19} + 130806 q^{20} + 3453 q^{21} - 10785 q^{22} + 111999 q^{23} - 330189 q^{24} + 168791 q^{25} + 158760 q^{27} + 490908 q^{28} + 198183 q^{29} - 368442 q^{30} - 94565 q^{31} - 308913 q^{32} - 640731 q^{33} - 811075 q^{34} - 587310 q^{35} + 221439 q^{36} - 376302 q^{37} - 252909 q^{38} + 76641 q^{39} + 3010250 q^{40} + 2282655 q^{41} - 952236 q^{42} + 131917 q^{43} - 721677 q^{45} - 1878624 q^{46} - 1029987 q^{47} - 2579451 q^{48} + 494659 q^{49} - 605697 q^{50} - 967464 q^{51} + 6289652 q^{52} + 1135824 q^{53} + 1785603 q^{54} - 3133494 q^{55} - 3655998 q^{56} - 809760 q^{57} - 10949326 q^{58} + 3053271 q^{59} + 3404058 q^{60} + 4293885 q^{61} + 4217721 q^{63} + 18425866 q^{64} + 3068145 q^{65} - 2771214 q^{66} + 940987 q^{67} + 5210877 q^{68} + 1372605 q^{69} - 28101636 q^{70} - 10350744 q^{71} - 1728093 q^{72} - 12162498 q^{73} - 1590654 q^{74} - 4432044 q^{75} + 36314961 q^{76} + 5159997 q^{77} + 9860532 q^{78} + 12337093 q^{79} + 9836142 q^{81} - 41874106 q^{82} + 2315637 q^{83} + 1298838 q^{84} + 16268962 q^{85} + 16265685 q^{86} - 24976413 q^{87} + 32199891 q^{88} - 42615600 q^{89} - 14605122 q^{90} - 11014174 q^{91} + 17059596 q^{92} - 47647503 q^{93} - 34456128 q^{94} + 2553996 q^{95} - 13783884 q^{96} + 21800193 q^{97} + 69035013 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.8.a \(\chi_{36}(1, \cdot)\) 36.8.a.a 1 1
36.8.a.b 1
36.8.a.c 1
36.8.b \(\chi_{36}(35, \cdot)\) 36.8.b.a 2 1
36.8.b.b 12
36.8.e \(\chi_{36}(13, \cdot)\) 36.8.e.a 14 2
36.8.h \(\chi_{36}(11, \cdot)\) 36.8.h.a 80 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(36)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)