## Defining parameters

 Level: $$N$$ = $$268 = 2^{2} \cdot 67$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$8$$ Newforms: $$10$$ Sturm bound: $$8976$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(268))$$.

Total New Old
Modular forms 2409 1375 1034
Cusp forms 2080 1243 837
Eisenstein series 329 132 197

## Trace form

 $$1243q - 33q^{2} - 33q^{4} - 66q^{5} - 33q^{6} - 33q^{8} - 66q^{9} + O(q^{10})$$ $$1243q - 33q^{2} - 33q^{4} - 66q^{5} - 33q^{6} - 33q^{8} - 66q^{9} - 33q^{10} - 33q^{12} - 66q^{13} - 33q^{14} - 33q^{16} - 66q^{17} - 33q^{18} - 33q^{20} - 66q^{21} - 33q^{22} - 33q^{24} - 66q^{25} - 33q^{26} - 33q^{28} - 66q^{29} - 33q^{30} - 33q^{32} - 66q^{33} - 33q^{34} - 33q^{36} - 66q^{37} - 33q^{38} - 33q^{40} - 66q^{41} - 33q^{42} - 33q^{44} - 66q^{45} - 33q^{46} - 33q^{48} - 66q^{49} - 33q^{50} - 33q^{52} - 99q^{53} - 33q^{54} - 99q^{55} - 33q^{56} - 143q^{57} - 33q^{58} - 66q^{59} - 33q^{60} - 198q^{61} - 33q^{62} - 143q^{63} - 33q^{64} - 198q^{65} - 66q^{67} - 66q^{68} - 132q^{69} - 33q^{70} - 132q^{71} - 33q^{72} - 209q^{73} - 33q^{74} - 132q^{75} - 33q^{76} - 132q^{77} - 33q^{78} - 77q^{79} - 33q^{80} - 165q^{81} - 33q^{82} - 33q^{83} - 33q^{84} - 66q^{85} - 33q^{86} - 33q^{88} - 66q^{89} - 33q^{90} - 33q^{92} - 66q^{93} - 33q^{94} - 33q^{96} - 66q^{97} - 33q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(268))$$

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
268.2.a $$\chi_{268}(1, \cdot)$$ 268.2.a.a 1 1
268.2.a.b 2
268.2.a.c 2
268.2.d $$\chi_{268}(267, \cdot)$$ 268.2.d.a 32 1
268.2.e $$\chi_{268}(29, \cdot)$$ 268.2.e.a 12 2
268.2.h $$\chi_{268}(231, \cdot)$$ 268.2.h.a 64 2
268.2.i $$\chi_{268}(9, \cdot)$$ 268.2.i.a 50 10
268.2.j $$\chi_{268}(3, \cdot)$$ 268.2.j.a 320 10
268.2.m $$\chi_{268}(17, \cdot)$$ 268.2.m.a 120 20
268.2.n $$\chi_{268}(7, \cdot)$$ 268.2.n.a 640 20

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(268))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(268)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(67))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(134))$$$$^{\oplus 2}$$