## 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

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

## 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

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