## Defining parameters

 Level: $$N$$ = $$207 = 3^{2} \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newform subspaces: $$18$$ Sturm bound: $$6336$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(207))$$.

Total New Old
Modular forms 1760 1343 417
Cusp forms 1409 1155 254
Eisenstein series 351 188 163

## Trace form

 $$1155 q - 33 q^{2} - 44 q^{3} - 33 q^{4} - 33 q^{5} - 44 q^{6} - 33 q^{7} - 33 q^{8} - 44 q^{9} + O(q^{10})$$ $$1155 q - 33 q^{2} - 44 q^{3} - 33 q^{4} - 33 q^{5} - 44 q^{6} - 33 q^{7} - 33 q^{8} - 44 q^{9} - 99 q^{10} - 33 q^{11} - 44 q^{12} - 33 q^{13} - 33 q^{14} - 44 q^{15} - 55 q^{16} - 44 q^{17} - 44 q^{18} - 110 q^{19} - 77 q^{20} - 44 q^{21} - 66 q^{22} - 55 q^{23} - 88 q^{24} - 55 q^{25} - 55 q^{26} - 44 q^{27} - 143 q^{28} - 44 q^{29} - 44 q^{30} - 44 q^{31} - 55 q^{32} - 44 q^{33} - 55 q^{34} - 55 q^{35} - 44 q^{36} - 143 q^{37} - 88 q^{38} - 44 q^{39} - 121 q^{40} - 55 q^{41} - 44 q^{42} - 77 q^{43} - 44 q^{44} - 44 q^{45} - 187 q^{46} - 110 q^{47} - 44 q^{48} - 99 q^{49} - 110 q^{50} - 44 q^{51} - 143 q^{52} - 55 q^{53} - 77 q^{55} + 110 q^{56} + 22 q^{57} + 44 q^{58} + 77 q^{59} + 176 q^{60} + 99 q^{61} + 165 q^{62} + 66 q^{63} + 165 q^{64} + 198 q^{65} + 132 q^{66} + 33 q^{67} + 396 q^{68} + 66 q^{69} + 198 q^{70} + 132 q^{71} + 220 q^{72} - 33 q^{73} + 220 q^{74} + 110 q^{75} + 176 q^{76} + 88 q^{77} + 88 q^{78} + 55 q^{79} + 198 q^{80} + 44 q^{81} - 33 q^{82} + 22 q^{83} + 88 q^{84} - 77 q^{85} - 77 q^{86} - 44 q^{87} - 165 q^{88} - 99 q^{89} - 198 q^{91} - 132 q^{92} - 88 q^{93} - 154 q^{94} - 132 q^{95} + 44 q^{96} - 132 q^{97} - 165 q^{98} - 44 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(207))$$

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
207.2.a $$\chi_{207}(1, \cdot)$$ 207.2.a.a 1 1
207.2.a.b 2
207.2.a.c 2
207.2.a.d 2
207.2.a.e 2
207.2.c $$\chi_{207}(206, \cdot)$$ 207.2.c.a 8 1
207.2.e $$\chi_{207}(70, \cdot)$$ 207.2.e.a 16 2
207.2.e.b 28
207.2.g $$\chi_{207}(68, \cdot)$$ 207.2.g.a 12 2
207.2.g.b 32
207.2.i $$\chi_{207}(55, \cdot)$$ 207.2.i.a 10 10
207.2.i.b 10
207.2.i.c 10
207.2.i.d 20
207.2.i.e 40
207.2.k $$\chi_{207}(17, \cdot)$$ 207.2.k.a 80 10
207.2.m $$\chi_{207}(4, \cdot)$$ 207.2.m.a 440 20
207.2.o $$\chi_{207}(5, \cdot)$$ 207.2.o.a 440 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(207))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(207)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(69))$$$$^{\oplus 2}$$