# Properties

 Label 13.4 Level 13 Weight 4 Dimension 15 Nonzero newspaces 4 Newform subspaces 7 Sturm bound 56 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$4$$ Newform subspaces: $$7$$ Sturm bound: $$56$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(13))$$.

Total New Old
Modular forms 27 25 2
Cusp forms 15 15 0
Eisenstein series 12 10 2

## Trace form

 $$15 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 42 q^{7} - 78 q^{8} - 6 q^{9} + O(q^{10})$$ $$15 q - 6 q^{2} - 6 q^{3} - 6 q^{4} - 6 q^{5} - 6 q^{6} - 42 q^{7} - 78 q^{8} - 6 q^{9} + 84 q^{10} + 54 q^{11} + 228 q^{12} + 138 q^{13} + 108 q^{14} + 66 q^{15} - 6 q^{16} - 195 q^{17} - 834 q^{18} - 450 q^{19} - 522 q^{20} - 6 q^{21} + 384 q^{22} + 222 q^{23} + 1050 q^{24} + 363 q^{25} + 744 q^{26} + 816 q^{27} - 60 q^{28} - 435 q^{29} - 582 q^{30} - 318 q^{31} - 660 q^{32} - 606 q^{33} - 702 q^{34} - 6 q^{35} - 162 q^{36} + 177 q^{37} + 1356 q^{38} + 66 q^{39} - 228 q^{40} - 477 q^{41} - 636 q^{42} - 426 q^{43} + 228 q^{44} + 279 q^{45} + 822 q^{46} + 126 q^{47} - 390 q^{48} + 966 q^{49} - 102 q^{50} - 396 q^{51} - 336 q^{52} + 936 q^{53} + 720 q^{54} + 1398 q^{55} + 996 q^{56} + 1158 q^{57} + 1020 q^{58} + 486 q^{59} + 1152 q^{60} - 1137 q^{61} - 2622 q^{62} - 3186 q^{63} - 4692 q^{64} - 4065 q^{65} - 4152 q^{66} - 918 q^{67} + 1320 q^{68} + 2022 q^{69} + 1980 q^{70} + 1938 q^{71} + 2940 q^{72} + 2154 q^{73} + 2568 q^{74} + 612 q^{75} - 1842 q^{76} + 372 q^{77} + 2940 q^{78} - 972 q^{79} + 3384 q^{80} + 456 q^{81} + 3552 q^{82} + 3426 q^{83} + 2268 q^{84} + 1011 q^{85} - 2808 q^{86} - 3906 q^{87} - 444 q^{88} - 3726 q^{89} - 6936 q^{90} - 2730 q^{91} - 4812 q^{92} - 4194 q^{93} - 1722 q^{94} - 1962 q^{95} + 1548 q^{96} + 1806 q^{97} - 2730 q^{98} + 5190 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(13))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
13.4.a $$\chi_{13}(1, \cdot)$$ 13.4.a.a 1 1
13.4.a.b 2
13.4.b $$\chi_{13}(12, \cdot)$$ 13.4.b.a 2 1
13.4.c $$\chi_{13}(3, \cdot)$$ 13.4.c.a 2 2
13.4.c.b 4
13.4.e $$\chi_{13}(4, \cdot)$$ 13.4.e.a 2 2
13.4.e.b 2