## Defining parameters

 Level: $$N$$ = $$21 = 3 \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$3$$ Newform subspaces: $$3$$ Sturm bound: $$64$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(21))$$.

Total New Old
Modular forms 28 17 11
Cusp forms 5 5 0
Eisenstein series 23 12 11

## Trace form

 $$5 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 3 q^{6} - 5 q^{7} + 3 q^{8} + 3 q^{9} + O(q^{10})$$ $$5 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 3 q^{6} - 5 q^{7} + 3 q^{8} + 3 q^{9} + 6 q^{10} + 6 q^{11} + 3 q^{12} + 3 q^{14} - 6 q^{15} - q^{16} - 6 q^{17} - 3 q^{18} - 6 q^{19} - 6 q^{20} - 3 q^{21} - 12 q^{22} + 3 q^{24} + 5 q^{25} + 3 q^{27} + 17 q^{28} + 6 q^{29} + 6 q^{30} + 6 q^{31} + 3 q^{32} + 6 q^{33} + 6 q^{34} - 9 q^{36} + 2 q^{37} - 6 q^{38} - 6 q^{40} - 18 q^{41} - 9 q^{42} - 4 q^{43} + 6 q^{47} - 9 q^{48} - q^{49} - 3 q^{50} - 6 q^{51} - 6 q^{52} - 6 q^{53} - 3 q^{54} - 3 q^{56} + 24 q^{57} - 6 q^{58} + 24 q^{59} + 6 q^{60} + 36 q^{62} + 15 q^{63} + 7 q^{64} + 6 q^{65} - 2 q^{67} + 6 q^{68} - 18 q^{70} - 12 q^{71} + 3 q^{72} - 30 q^{73} - 12 q^{74} - 15 q^{75} - 12 q^{77} + 6 q^{78} - 2 q^{79} - 6 q^{80} - 9 q^{81} + 18 q^{82} - 3 q^{84} + 12 q^{85} - 6 q^{86} - 6 q^{87} + 12 q^{88} - 30 q^{89} - 6 q^{90} + 6 q^{91} - 24 q^{93} + 12 q^{94} - 6 q^{95} + 3 q^{96} + 6 q^{97} + 3 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$

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
21.2.a $$\chi_{21}(1, \cdot)$$ 21.2.a.a 1 1
21.2.c $$\chi_{21}(20, \cdot)$$ None 0 1
21.2.e $$\chi_{21}(4, \cdot)$$ 21.2.e.a 2 2
21.2.g $$\chi_{21}(5, \cdot)$$ 21.2.g.a 2 2