# Properties

 Label 16.3 Level 16 Weight 3 Dimension 7 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 48 Trace bound 1

# Learn more about

## Defining parameters

 Level: $$N$$ = $$16 = 2^{4}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$48$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(16))$$.

Total New Old
Modular forms 23 11 12
Cusp forms 9 7 2
Eisenstein series 14 4 10

## Trace form

 $$7q - 2q^{2} - 2q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 4q^{7} + 4q^{8} + 9q^{9} + O(q^{10})$$ $$7q - 2q^{2} - 2q^{3} - 8q^{4} - 8q^{5} - 8q^{6} - 4q^{7} + 4q^{8} + 9q^{9} + 36q^{10} - 18q^{11} + 52q^{12} + 8q^{13} + 12q^{14} - 40q^{16} - 34q^{17} - 74q^{18} + 30q^{19} - 84q^{20} - 20q^{21} - 52q^{22} + 60q^{23} + 48q^{24} + 11q^{25} + 96q^{26} + 64q^{27} + 56q^{28} + 24q^{29} + 52q^{30} + 8q^{32} - 4q^{33} - 76q^{34} - 100q^{35} - 52q^{36} - 24q^{37} + 40q^{38} - 196q^{39} + 40q^{40} + 18q^{41} - 24q^{42} - 114q^{43} + 20q^{44} + 12q^{45} + 28q^{46} - 24q^{48} + 3q^{49} + 46q^{50} + 156q^{51} + 100q^{52} + 168q^{53} + 32q^{54} + 252q^{55} - 168q^{56} - 176q^{58} + 206q^{59} - 160q^{60} + 8q^{61} - 144q^{62} + 64q^{64} - 48q^{65} + 196q^{66} - 226q^{67} + 112q^{68} - 116q^{69} - 16q^{70} - 260q^{71} + 52q^{72} - 110q^{73} - 92q^{74} - 238q^{75} - 188q^{76} - 212q^{77} - 84q^{78} + 232q^{80} + 167q^{81} + 304q^{82} + 318q^{83} + 232q^{84} - 32q^{85} + 268q^{86} + 444q^{87} - 8q^{88} - 78q^{89} - 160q^{90} + 188q^{91} - 168q^{92} - 32q^{93} + 48q^{94} - 80q^{96} + 126q^{97} + 10q^{98} - 226q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(16))$$

We only show spaces with odd 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
16.3.c $$\chi_{16}(15, \cdot)$$ 16.3.c.a 1 1
16.3.d $$\chi_{16}(7, \cdot)$$ None 0 1
16.3.f $$\chi_{16}(3, \cdot)$$ 16.3.f.a 6 2

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(16))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(16)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 2}$$