# Properties

 Label 26.2 Level 26 Weight 2 Dimension 6 Nonzero newspaces 3 Newform subspaces 4 Sturm bound 84 Trace bound 4

## 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

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

## 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 available 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

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