Properties

 Label 108.4 Level 108 Weight 4 Dimension 432 Nonzero newspaces 6 Newform subspaces 11 Sturm bound 2592 Trace bound 1

Defining parameters

 Level: $$N$$ = $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$11$$ Sturm bound: $$2592$$ Trace bound: $$1$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(108))$$.

Total New Old
Modular forms 1047 464 583
Cusp forms 897 432 465
Eisenstein series 150 32 118

Trace form

 $$432 q - 3 q^{2} - 13 q^{4} - 6 q^{6} - 28 q^{7} - 9 q^{8} - 60 q^{9} + O(q^{10})$$ $$432 q - 3 q^{2} - 13 q^{4} - 6 q^{6} - 28 q^{7} - 9 q^{8} - 60 q^{9} + 43 q^{10} - 138 q^{11} - 123 q^{12} - 24 q^{13} + 147 q^{14} + 234 q^{15} + 131 q^{16} + 408 q^{17} + 351 q^{18} + 170 q^{19} + 459 q^{20} - 24 q^{21} + 195 q^{22} - 114 q^{23} - 300 q^{24} - 887 q^{25} + 27 q^{27} - 6 q^{28} - 312 q^{29} - 207 q^{30} + 92 q^{31} - 1383 q^{32} + 921 q^{33} - 905 q^{34} + 1110 q^{35} - 1056 q^{36} + 828 q^{37} - 1791 q^{38} + 66 q^{39} - 725 q^{40} + 264 q^{41} + 2574 q^{42} - 1492 q^{43} + 2655 q^{44} - 978 q^{45} + 1101 q^{46} - 2070 q^{47} - 435 q^{48} + 407 q^{49} - 852 q^{50} - 1368 q^{51} + 2167 q^{52} + 1140 q^{53} - 4458 q^{54} + 918 q^{55} + 81 q^{56} - 609 q^{57} + 2455 q^{58} - 1671 q^{59} + 966 q^{60} - 2040 q^{61} + 1872 q^{62} + 30 q^{63} - 163 q^{64} - 2412 q^{65} + 3093 q^{66} - 3502 q^{67} - 2634 q^{68} - 96 q^{69} - 6333 q^{70} - 240 q^{71} - 4524 q^{72} - 360 q^{73} - 11757 q^{74} + 732 q^{75} - 5121 q^{76} + 378 q^{77} - 2976 q^{78} + 3356 q^{79} + 3792 q^{81} + 2614 q^{82} + 5076 q^{83} + 6324 q^{84} + 5018 q^{85} + 16653 q^{86} + 4824 q^{87} + 10251 q^{88} + 9165 q^{89} - 1104 q^{90} + 2278 q^{91} + 5469 q^{92} + 8568 q^{93} + 6351 q^{94} + 534 q^{95} + 582 q^{96} - 504 q^{97} + 2898 q^{98} - 5076 q^{99} + O(q^{100})$$

Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(108))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
108.4.a $$\chi_{108}(1, \cdot)$$ 108.4.a.a 1 1
108.4.a.b 1
108.4.a.c 1
108.4.a.d 1
108.4.b $$\chi_{108}(107, \cdot)$$ 108.4.b.a 12 1
108.4.b.b 12
108.4.e $$\chi_{108}(37, \cdot)$$ 108.4.e.a 6 2
108.4.h $$\chi_{108}(35, \cdot)$$ 108.4.h.a 8 2
108.4.h.b 24
108.4.i $$\chi_{108}(13, \cdot)$$ 108.4.i.a 54 6
108.4.l $$\chi_{108}(11, \cdot)$$ 108.4.l.a 312 6

Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(108))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(108)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 8}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 9}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(27))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(36))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(54))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(108))$$$$^{\oplus 1}$$