# Properties

 Label 44.4 Level 44 Weight 4 Dimension 95 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 480 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$44 = 2^{2} \cdot 11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$480$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(44))$$.

Total New Old
Modular forms 205 115 90
Cusp forms 155 95 60
Eisenstein series 50 20 30

## Trace form

 $$95 q - 5 q^{2} - 5 q^{4} - 10 q^{5} - 5 q^{6} - 10 q^{7} - 5 q^{8} + 70 q^{9} + O(q^{10})$$ $$95 q - 5 q^{2} - 5 q^{4} - 10 q^{5} - 5 q^{6} - 10 q^{7} - 5 q^{8} + 70 q^{9} + 50 q^{11} - 10 q^{12} + 10 q^{13} + 170 q^{14} + 110 q^{15} + 175 q^{16} - 180 q^{17} - 230 q^{18} - 225 q^{19} - 480 q^{20} - 420 q^{21} - 635 q^{22} - 480 q^{23} - 455 q^{24} - 430 q^{25} - 30 q^{26} + 165 q^{27} + 520 q^{28} + 640 q^{29} + 880 q^{30} + 990 q^{31} + 1795 q^{33} - 950 q^{34} + 940 q^{35} - 390 q^{36} + 70 q^{37} + 320 q^{38} - 610 q^{39} + 1080 q^{40} - 1720 q^{41} + 2290 q^{42} - 1990 q^{43} + 1500 q^{44} - 4050 q^{45} + 1330 q^{46} - 340 q^{47} + 1260 q^{48} + 200 q^{49} + 655 q^{50} + 1825 q^{51} + 1610 q^{52} + 4470 q^{53} + 2870 q^{55} - 1020 q^{56} + 3315 q^{57} - 1200 q^{58} - 295 q^{59} - 3080 q^{60} - 1490 q^{61} - 3980 q^{62} - 4400 q^{63} - 3785 q^{64} - 4280 q^{65} - 4230 q^{66} - 4190 q^{67} - 3840 q^{68} - 2920 q^{69} - 4420 q^{70} - 480 q^{71} - 5555 q^{72} - 460 q^{73} - 1890 q^{74} + 3835 q^{75} + 3580 q^{77} + 4360 q^{78} + 3390 q^{79} + 7500 q^{80} + 4325 q^{81} + 6985 q^{82} - 415 q^{83} + 6530 q^{84} - 410 q^{85} + 3355 q^{86} - 1700 q^{87} + 6955 q^{88} + 230 q^{89} + 10080 q^{90} + 1580 q^{91} + 7920 q^{92} + 4780 q^{93} + 7280 q^{94} + 4130 q^{95} + 5720 q^{96} + 3755 q^{97} + 3970 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$

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
44.4.a $$\chi_{44}(1, \cdot)$$ 44.4.a.a 1 1
44.4.a.b 2
44.4.c $$\chi_{44}(43, \cdot)$$ 44.4.c.a 16 1
44.4.e $$\chi_{44}(5, \cdot)$$ 44.4.e.a 12 4
44.4.g $$\chi_{44}(7, \cdot)$$ 44.4.g.a 64 4

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(44))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(44)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 3}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 1}$$