↑

Properties

Label 36.6
Level 36
Weight 6
Dimension 78
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 432
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(432\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(36))\).

Total New Old
Modular forms 200 86 114
Cusp forms 160 78 82
Eisenstein series 40 8 32

Trace form

\( 78 q - 3 q^{2} + 12 q^{3} - 21 q^{4} - 81 q^{5} - 27 q^{6} + 177 q^{7} + 30 q^{9} + O(q^{10}) \) \( 78 q - 3 q^{2} + 12 q^{3} - 21 q^{4} - 81 q^{5} - 27 q^{6} + 177 q^{7} + 30 q^{9} + 600 q^{10} - 363 q^{11} - 486 q^{12} + 369 q^{13} - 1518 q^{14} + 117 q^{15} - 2169 q^{16} + 1686 q^{17} + 1992 q^{18} - 1428 q^{19} - 1242 q^{20} + 123 q^{21} + 10047 q^{22} + 4503 q^{23} + 2235 q^{24} + 864 q^{25} - 7128 q^{27} - 25284 q^{28} - 17385 q^{29} - 6882 q^{30} - 3309 q^{31} - 7233 q^{32} + 26643 q^{33} + 53997 q^{34} + 41898 q^{35} + 6399 q^{36} - 540 q^{37} - 14877 q^{38} + 5529 q^{39} - 78078 q^{40} - 79197 q^{41} + 18564 q^{42} - 13983 q^{43} - 64131 q^{45} + 57600 q^{46} - 23859 q^{47} - 5931 q^{48} + 102462 q^{49} + 38631 q^{50} + 90612 q^{51} - 55764 q^{52} + 97350 q^{53} + 37587 q^{54} + 43938 q^{55} + 21186 q^{56} - 63852 q^{57} + 78738 q^{58} - 82869 q^{59} + 60930 q^{60} - 136287 q^{61} - 198255 q^{63} - 186486 q^{64} - 89865 q^{65} - 47838 q^{66} + 183 q^{67} + 31413 q^{68} + 212571 q^{69} - 17892 q^{70} + 276240 q^{71} - 130941 q^{72} + 286068 q^{73} - 20406 q^{74} + 44640 q^{75} + 76881 q^{76} - 138285 q^{77} - 96684 q^{78} - 147483 q^{79} - 418962 q^{81} - 263610 q^{82} - 296667 q^{83} + 141630 q^{84} - 393030 q^{85} + 279237 q^{86} + 397323 q^{87} + 226515 q^{88} + 568578 q^{89} + 235278 q^{90} + 445386 q^{91} + 435804 q^{92} + 321879 q^{93} - 223752 q^{94} - 439908 q^{95} - 37476 q^{96} + 277113 q^{97} - 697239 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)

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
36.6.a \(\chi_{36}(1, \cdot)\) 36.6.a.a 1 1
36.6.a.b 1
36.6.b \(\chi_{36}(35, \cdot)\) 36.6.b.a 2 1
36.6.b.b 8
36.6.e \(\chi_{36}(13, \cdot)\) 36.6.e.a 10 2
36.6.h \(\chi_{36}(11, \cdot)\) 36.6.h.a 56 2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(36))\) into lower level spaces

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