Defining parameters

 Level: $$N$$ = $$21 = 3 \cdot 7$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$4$$ Newform subspaces: $$7$$ Sturm bound: $$96$$ Trace bound: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(21))$$.

Total New Old
Modular forms 44 26 18
Cusp forms 20 18 2
Eisenstein series 24 8 16

Trace form

 $$18 q - 6 q^{3} - 22 q^{4} - 6 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} - 24 q^{9} + O(q^{10})$$ $$18 q - 6 q^{3} - 22 q^{4} - 6 q^{5} - 6 q^{6} + 2 q^{7} - 6 q^{8} - 24 q^{9} - 12 q^{10} + 6 q^{11} + 18 q^{12} + 2 q^{13} + 24 q^{14} + 48 q^{15} + 90 q^{16} + 48 q^{17} + 96 q^{18} + 2 q^{19} - 24 q^{21} - 108 q^{22} - 96 q^{23} - 150 q^{24} - 132 q^{25} - 126 q^{26} - 132 q^{27} - 102 q^{28} - 12 q^{29} + 24 q^{30} + 86 q^{31} + 78 q^{32} + 186 q^{33} + 240 q^{34} + 210 q^{35} + 198 q^{36} + 160 q^{37} + 174 q^{38} + 66 q^{39} + 96 q^{40} - 72 q^{42} - 188 q^{43} - 168 q^{44} - 198 q^{45} - 204 q^{46} - 222 q^{47} - 210 q^{48} - 120 q^{49} - 114 q^{50} - 168 q^{51} + 152 q^{52} - 12 q^{53} - 84 q^{54} + 156 q^{55} + 18 q^{56} + 108 q^{57} + 84 q^{59} + 96 q^{60} + 38 q^{61} + 78 q^{63} - 34 q^{64} + 18 q^{65} - 36 q^{66} + 102 q^{67} + 36 q^{68} + 288 q^{69} - 60 q^{70} + 120 q^{71} + 174 q^{72} - 100 q^{73} + 90 q^{74} + 180 q^{75} - 292 q^{76} + 72 q^{77} + 24 q^{78} + 162 q^{79} + 48 q^{80} + 108 q^{82} + 102 q^{84} - 168 q^{85} + 210 q^{86} + 12 q^{87} - 24 q^{88} - 60 q^{89} - 132 q^{90} - 148 q^{91} - 84 q^{92} - 264 q^{93} - 324 q^{94} - 438 q^{95} - 402 q^{96} - 376 q^{97} - 270 q^{98} - 432 q^{99} + O(q^{100})$$

Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(21))$$

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
21.3.b $$\chi_{21}(8, \cdot)$$ 21.3.b.a 4 1
21.3.d $$\chi_{21}(13, \cdot)$$ 21.3.d.a 2 1
21.3.f $$\chi_{21}(10, \cdot)$$ 21.3.f.a 2 2
21.3.f.b 2
21.3.f.c 2
21.3.h $$\chi_{21}(2, \cdot)$$ 21.3.h.a 2 2
21.3.h.b 4

Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(21))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(21)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 2}$$