## 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

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

## 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 the 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

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