# Properties

 Label 13.6 Level 13 Weight 6 Dimension 29 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 84 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$13$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$84$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(13))$$.

Total New Old
Modular forms 41 39 2
Cusp forms 29 29 0
Eisenstein series 12 10 2

## Trace form

 $$29 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 304 q^{7} + 570 q^{8} + 642 q^{9} + O(q^{10})$$ $$29 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 304 q^{7} + 570 q^{8} + 642 q^{9} + 54 q^{10} - 540 q^{11} - 2892 q^{12} - 1578 q^{13} - 540 q^{14} + 1182 q^{15} + 5114 q^{16} - 1203 q^{17} + 3432 q^{18} + 4982 q^{19} + 5490 q^{20} + 3660 q^{21} + 864 q^{22} - 3234 q^{23} - 24438 q^{24} - 9387 q^{25} - 17976 q^{26} - 15168 q^{27} - 22540 q^{28} + 159 q^{29} + 53130 q^{30} + 29816 q^{31} + 79260 q^{32} + 41316 q^{33} + 18354 q^{34} - 19536 q^{35} - 95346 q^{36} - 35995 q^{37} - 51996 q^{38} - 76998 q^{39} - 95844 q^{40} - 2727 q^{41} + 66108 q^{42} + 84460 q^{43} + 136884 q^{44} + 134919 q^{45} + 105414 q^{46} + 42696 q^{47} + 17034 q^{48} - 70052 q^{49} - 200964 q^{50} - 252180 q^{51} - 242500 q^{52} - 57348 q^{53} + 34920 q^{54} + 37248 q^{55} + 144276 q^{56} + 152748 q^{57} + 175830 q^{58} + 95760 q^{59} + 176112 q^{60} + 180189 q^{61} - 218694 q^{62} - 206640 q^{63} - 199380 q^{64} - 77307 q^{65} - 124536 q^{66} - 80158 q^{67} + 343716 q^{68} + 149208 q^{69} + 245556 q^{70} + 99822 q^{71} + 248604 q^{72} - 45730 q^{73} - 287574 q^{74} - 155904 q^{75} - 89746 q^{76} - 120840 q^{77} - 452892 q^{78} + 17160 q^{79} - 348408 q^{80} - 209730 q^{81} + 68418 q^{82} + 99132 q^{83} + 135660 q^{84} - 79383 q^{85} + 64296 q^{86} - 7758 q^{87} + 236484 q^{88} + 384570 q^{89} + 913152 q^{90} + 449384 q^{91} + 197076 q^{92} + 404976 q^{93} - 308370 q^{94} - 273330 q^{95} - 577764 q^{96} - 197518 q^{97} - 597306 q^{98} - 367068 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(13))$$

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
13.6.a $$\chi_{13}(1, \cdot)$$ 13.6.a.a 2 1
13.6.a.b 3
13.6.b $$\chi_{13}(12, \cdot)$$ 13.6.b.a 6 1
13.6.c $$\chi_{13}(3, \cdot)$$ 13.6.c.a 8 2
13.6.e $$\chi_{13}(4, \cdot)$$ 13.6.e.a 10 2