# Properties

 Label 13.5 Level 13 Weight 5 Dimension 22 Nonzero newspaces 2 Newforms 2 Sturm bound 70 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$13$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$2$$ Newforms: $$2$$ Sturm bound: $$70$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(13))$$.

Total New Old
Modular forms 34 34 0
Cusp forms 22 22 0
Eisenstein series 12 12 0

## Trace form

 $$22q - 6q^{2} - 6q^{3} - 6q^{4} - 6q^{5} - 6q^{6} + 104q^{7} - 6q^{8} - 222q^{9} + O(q^{10})$$ $$22q - 6q^{2} - 6q^{3} - 6q^{4} - 6q^{5} - 6q^{6} + 104q^{7} - 6q^{8} - 222q^{9} - 486q^{10} - 132q^{11} + 294q^{13} + 564q^{14} + 750q^{15} + 1274q^{16} + 984q^{17} + 1632q^{18} - 766q^{19} - 3534q^{20} - 3204q^{21} - 3156q^{22} - 1014q^{23} - 2166q^{24} + 1524q^{26} + 3588q^{27} + 7648q^{28} + 4998q^{29} + 9162q^{30} + 592q^{31} - 2904q^{32} - 3312q^{33} - 7806q^{34} - 9096q^{35} - 15750q^{36} - 3548q^{37} + 8178q^{39} + 18108q^{40} + 9030q^{41} + 8328q^{42} - 1368q^{43} + 6780q^{44} - 5976q^{45} - 14730q^{46} - 5388q^{47} - 12438q^{48} - 11820q^{49} - 13896q^{50} + 5332q^{52} + 9312q^{53} + 13056q^{54} + 13344q^{55} + 8124q^{56} + 6936q^{57} + 9546q^{58} + 1992q^{59} - 5148q^{60} + 5826q^{61} + 19614q^{62} + 11352q^{63} - 10266q^{65} - 28464q^{66} - 14782q^{67} - 17016q^{68} + 2412q^{69} - 27156q^{70} - 22722q^{71} + 7440q^{72} - 9574q^{73} - 1338q^{74} + 8280q^{75} + 14198q^{76} - 5952q^{78} - 14448q^{79} - 9516q^{80} - 17322q^{81} - 5346q^{82} + 32052q^{83} + 32244q^{84} + 39546q^{85} + 96636q^{86} + 64926q^{87} + 40836q^{88} + 19506q^{89} - 21892q^{91} - 44580q^{92} - 88440q^{93} - 66762q^{94} - 98574q^{95} - 73944q^{96} + 27790q^{97} + 20058q^{98} - 4140q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(13))$$

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
13.5.d $$\chi_{13}(5, \cdot)$$ 13.5.d.a 6 2
13.5.f $$\chi_{13}(2, \cdot)$$ 13.5.f.a 16 4