## Defining parameters

 Level: $$N$$ = $$26 = 2 \cdot 13$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$126$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(26))$$.

Total New Old
Modular forms 54 14 40
Cusp forms 30 14 16
Eisenstein series 24 0 24

## Trace form

 $$14 q - 20 q^{7} - 12 q^{8} - 48 q^{9} + O(q^{10})$$ $$14 q - 20 q^{7} - 12 q^{8} - 48 q^{9} - 30 q^{10} - 12 q^{11} + 24 q^{13} + 24 q^{14} + 72 q^{15} + 16 q^{16} + 36 q^{17} + 90 q^{18} + 40 q^{19} + 24 q^{20} - 60 q^{21} - 24 q^{23} + 72 q^{27} - 40 q^{28} - 156 q^{29} - 192 q^{30} - 124 q^{31} + 12 q^{33} - 96 q^{34} - 60 q^{35} - 48 q^{36} + 8 q^{37} + 114 q^{41} + 144 q^{42} + 12 q^{43} + 144 q^{44} + 330 q^{45} + 192 q^{46} + 276 q^{47} + 300 q^{49} + 246 q^{50} + 20 q^{52} - 240 q^{53} - 360 q^{54} - 228 q^{55} - 96 q^{56} - 396 q^{57} - 162 q^{58} - 84 q^{59} - 96 q^{60} + 78 q^{61} - 72 q^{62} - 228 q^{63} - 342 q^{65} + 96 q^{66} - 32 q^{67} + 12 q^{68} + 132 q^{69} + 216 q^{70} - 120 q^{71} + 192 q^{72} + 64 q^{73} + 78 q^{74} + 120 q^{75} - 80 q^{76} + 216 q^{78} - 120 q^{79} + 48 q^{80} + 132 q^{81} - 330 q^{82} + 108 q^{83} - 168 q^{84} - 30 q^{85} - 96 q^{86} + 264 q^{87} + 216 q^{89} + 388 q^{91} + 48 q^{92} + 492 q^{93} + 240 q^{94} + 672 q^{95} + 128 q^{97} - 240 q^{98} + 36 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(26))$$

We only show spaces with odd 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
26.3.d $$\chi_{26}(5, \cdot)$$ 26.3.d.a 2 2
26.3.f $$\chi_{26}(7, \cdot)$$ 26.3.f.a 4 4
26.3.f.b 8

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(26))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(26)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 2}$$