## Defining parameters

 Level: $$N$$ = $$16 = 2^{4}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$1$$ Newforms: $$1$$ Sturm bound: $$32$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(16))$$.

Total New Old
Modular forms 15 7 8
Cusp forms 2 2 0
Eisenstein series 13 5 8

## Trace form

 $$2q - 2q^{2} - 2q^{3} - 2q^{5} + 4q^{6} + 4q^{8} + O(q^{10})$$ $$2q - 2q^{2} - 2q^{3} - 2q^{5} + 4q^{6} + 4q^{8} + 2q^{11} - 4q^{12} - 2q^{13} - 4q^{14} + 4q^{15} - 8q^{16} - 4q^{17} + 2q^{18} + 6q^{19} + 4q^{20} + 4q^{21} + 4q^{26} - 8q^{27} + 8q^{28} + 6q^{29} - 4q^{30} - 16q^{31} + 8q^{32} - 4q^{33} + 4q^{34} - 4q^{35} - 4q^{36} + 6q^{37} - 12q^{38} - 8q^{40} + 10q^{43} - 4q^{44} + 2q^{45} + 12q^{46} + 16q^{47} + 8q^{48} + 6q^{49} - 6q^{50} + 4q^{51} - 4q^{52} - 10q^{53} - 8q^{56} - 12q^{58} - 6q^{59} - 18q^{61} + 16q^{62} + 4q^{63} + 4q^{65} + 4q^{66} - 10q^{67} - 12q^{69} + 8q^{70} + 4q^{72} + 6q^{75} + 12q^{76} + 4q^{77} - 4q^{78} + 8q^{80} + 10q^{81} - 2q^{83} - 8q^{84} + 4q^{85} + 8q^{88} - 4q^{90} + 4q^{91} - 24q^{92} + 16q^{93} - 16q^{94} - 12q^{95} - 16q^{96} - 4q^{97} - 6q^{98} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$

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
16.2.a $$\chi_{16}(1, \cdot)$$ None 0 1
16.2.b $$\chi_{16}(9, \cdot)$$ None 0 1
16.2.e $$\chi_{16}(5, \cdot)$$ 16.2.e.a 2 2