## Defining parameters

 Level: $$N$$ = $$26 = 2 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$3$$ Newform subspaces: $$4$$ Sturm bound: $$84$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(26))$$.

Total New Old
Modular forms 33 6 27
Cusp forms 10 6 4
Eisenstein series 23 0 23

## Trace form

 $$6q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 4q^{7} + 2q^{8} + 3q^{9} + O(q^{10})$$ $$6q - q^{2} - 4q^{3} - q^{4} - 6q^{5} - 4q^{6} - 4q^{7} + 2q^{8} + 3q^{9} + 9q^{10} + 11q^{13} + 4q^{14} + 3q^{16} - 3q^{17} + 2q^{18} + 8q^{19} - 3q^{20} - 4q^{21} - 12q^{22} - 12q^{23} - 4q^{24} - 16q^{25} - 13q^{26} - 4q^{27} - 4q^{28} + 9q^{29} + 8q^{31} - q^{32} + 12q^{33} + 6q^{34} + 24q^{35} + 11q^{36} - 7q^{37} + 16q^{38} - 6q^{40} + 9q^{41} + 4q^{42} + 12q^{44} - 3q^{45} - 4q^{48} - 25q^{49} - 4q^{50} - 6q^{52} - 18q^{53} - 4q^{54} - 12q^{55} + 4q^{56} - 16q^{57} - 3q^{58} - 12q^{59} - 23q^{61} + 4q^{62} + 20q^{63} + 2q^{64} + 9q^{65} + 8q^{67} - 15q^{68} + 24q^{69} - 12q^{70} + 11q^{72} + 14q^{73} + q^{74} + 24q^{75} + 8q^{76} + 24q^{77} + 8q^{78} + 16q^{79} - 3q^{80} + 3q^{81} + 9q^{82} + 12q^{83} - 4q^{84} + 15q^{85} - 20q^{86} - 12q^{88} + 6q^{89} - 18q^{90} - 28q^{91} - 16q^{93} + 12q^{94} - 48q^{95} - 4q^{96} + 2q^{97} - 9q^{98} - 48q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$

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
26.2.a $$\chi_{26}(1, \cdot)$$ 26.2.a.a 1 1
26.2.a.b 1
26.2.b $$\chi_{26}(25, \cdot)$$ 26.2.b.a 2 1
26.2.c $$\chi_{26}(3, \cdot)$$ 26.2.c.a 2 2
26.2.e $$\chi_{26}(17, \cdot)$$ None 0 2

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(26))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(26)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$