Properties

Label 108.6
Level 108
Weight 6
Dimension 731
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 3888
Trace bound 1

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(3888\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(108))\).

Total New Old
Modular forms 1695 763 932
Cusp forms 1545 731 814
Eisenstein series 150 32 118

Trace form

\( 731 q - 3 q^{2} + 3 q^{4} - 72 q^{5} - 6 q^{6} - 2 q^{7} - 9 q^{8} + 318 q^{9} + O(q^{10}) \) \( 731 q - 3 q^{2} + 3 q^{4} - 72 q^{5} - 6 q^{6} - 2 q^{7} - 9 q^{8} + 318 q^{9} - 405 q^{10} - 1434 q^{11} + 1173 q^{12} + 568 q^{13} + 3027 q^{14} + 531 q^{15} - 2685 q^{16} - 5766 q^{17} - 5697 q^{18} - 209 q^{19} + 2475 q^{20} + 12882 q^{21} + 4803 q^{22} + 7707 q^{23} + 8988 q^{24} - 6736 q^{25} - 17415 q^{27} - 7206 q^{28} + 33375 q^{29} - 18135 q^{30} + 2896 q^{31} + 14457 q^{32} + 12342 q^{33} + 1431 q^{34} - 45375 q^{35} + 35664 q^{36} - 40325 q^{37} + 29745 q^{38} - 10545 q^{39} + 13419 q^{40} + 174162 q^{41} - 25506 q^{42} + 57448 q^{43} - 158049 q^{44} - 35781 q^{45} - 27651 q^{46} - 31932 q^{47} + 14469 q^{48} - 93090 q^{49} + 66756 q^{50} + 42831 q^{51} - 3465 q^{52} - 120990 q^{53} + 231414 q^{54} - 75942 q^{55} + 172449 q^{56} + 72048 q^{57} + 10743 q^{58} + 95925 q^{59} - 326058 q^{60} + 92380 q^{61} - 461448 q^{62} - 98115 q^{63} + 14637 q^{64} - 95976 q^{65} - 24771 q^{66} + 16903 q^{67} + 357870 q^{68} + 345801 q^{69} + 227715 q^{70} - 161556 q^{71} + 110388 q^{72} - 292772 q^{73} + 40803 q^{74} - 75273 q^{75} + 111135 q^{76} + 183600 q^{77} + 178248 q^{78} + 62164 q^{79} - 7926 q^{81} + 63030 q^{82} + 152226 q^{83} - 307308 q^{84} - 125652 q^{85} - 558483 q^{86} - 201483 q^{87} - 198645 q^{88} - 222162 q^{89} - 840048 q^{90} - 421192 q^{91} - 600627 q^{92} - 526815 q^{93} - 156753 q^{94} + 251274 q^{95} + 992022 q^{96} + 190771 q^{97} + 1307970 q^{98} + 13635 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(108))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
108.6.a \(\chi_{108}(1, \cdot)\) 108.6.a.a 1 1
108.6.a.b 2
108.6.a.c 2
108.6.a.d 2
108.6.b \(\chi_{108}(107, \cdot)\) 108.6.b.a 4 1
108.6.b.b 16
108.6.b.c 20
108.6.e \(\chi_{108}(37, \cdot)\) 108.6.e.a 10 2
108.6.h \(\chi_{108}(35, \cdot)\) 108.6.h.a 56 2
108.6.i \(\chi_{108}(13, \cdot)\) 108.6.i.a 90 6
108.6.l \(\chi_{108}(11, \cdot)\) 108.6.l.a 528 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(108))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(108)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 2}\)