## Defining parameters

 Level: $$N$$ = $$44 = 2^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$4$$ Sturm bound: $$240$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(44))$$.

Total New Old
Modular forms 85 45 40
Cusp forms 36 25 11
Eisenstein series 49 20 29

## Trace form

 $$25q - 5q^{2} - 5q^{4} - 10q^{5} - 5q^{6} - 5q^{7} - 5q^{8} - 20q^{9} + O(q^{10})$$ $$25q - 5q^{2} - 5q^{4} - 10q^{5} - 5q^{6} - 5q^{7} - 5q^{8} - 20q^{9} - 5q^{11} - 10q^{12} - 15q^{13} + 15q^{16} - 5q^{17} + 20q^{18} + 15q^{19} + 20q^{20} + 20q^{21} + 25q^{22} + 5q^{23} + 25q^{24} + 20q^{26} + 20q^{28} - 15q^{29} - 20q^{33} - 30q^{34} - 15q^{35} - 30q^{36} + 20q^{37} - 30q^{38} + 5q^{39} - 40q^{40} + 5q^{41} - 50q^{42} - 10q^{43} - 40q^{44} + 30q^{45} - 30q^{46} - 5q^{47} - 60q^{48} - 5q^{49} - 15q^{50} + 5q^{51} - 10q^{52} + 35q^{53} + 10q^{55} + 20q^{56} + 25q^{57} + 30q^{58} + 20q^{59} + 40q^{60} - 15q^{61} + 70q^{62} + 55q^{64} + 10q^{65} + 60q^{66} + 15q^{67} + 60q^{68} + 25q^{69} + 20q^{70} + 20q^{71} + 45q^{72} - 15q^{73} + 40q^{74} - 5q^{75} + 5q^{77} - 20q^{78} + 5q^{79} - 20q^{80} - 55q^{81} - 35q^{82} - 25q^{83} - 10q^{84} - 75q^{85} - 55q^{86} - 50q^{87} - 85q^{88} - 65q^{89} - 50q^{90} - 35q^{91} - 40q^{93} - 30q^{94} - 25q^{95} - 20q^{97} + 10q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
44.2.a $$\chi_{44}(1, \cdot)$$ 44.2.a.a 1 1
44.2.c $$\chi_{44}(43, \cdot)$$ 44.2.c.a 4 1
44.2.e $$\chi_{44}(5, \cdot)$$ 44.2.e.a 4 4
44.2.g $$\chi_{44}(7, \cdot)$$ 44.2.g.a 16 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(44))$$ into lower level spaces

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