# Properties

 Label 11.4 Level 11 Weight 4 Dimension 10 Nonzero newspaces 2 Newform subspaces 2 Sturm bound 40 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$11$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$40$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(11))$$.

Total New Old
Modular forms 20 18 2
Cusp forms 10 10 0
Eisenstein series 10 8 2

## Trace form

 $$10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 55 q^{6} - 15 q^{7} + 35 q^{8} + 75 q^{9} + O(q^{10})$$ $$10 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 55 q^{6} - 15 q^{7} + 35 q^{8} + 75 q^{9} + 90 q^{10} + 45 q^{11} + 150 q^{12} + 15 q^{13} - 200 q^{14} - 315 q^{15} - 385 q^{16} - 155 q^{17} - 10 q^{18} + 220 q^{19} + 430 q^{20} + 410 q^{21} + 625 q^{22} - 110 q^{23} - 195 q^{24} - 65 q^{25} - 180 q^{26} - 110 q^{27} - 170 q^{28} - 55 q^{29} - 380 q^{30} - 395 q^{31} + 220 q^{32} - 210 q^{33} - 350 q^{34} + 65 q^{35} + 40 q^{36} + 135 q^{37} + 380 q^{38} + 765 q^{39} + 40 q^{40} + 505 q^{41} + 30 q^{42} - 710 q^{43} - 1120 q^{44} + 880 q^{45} + 890 q^{46} + 585 q^{47} + 1420 q^{48} + 985 q^{49} + 85 q^{50} - 410 q^{51} - 1150 q^{52} - 1985 q^{53} - 3210 q^{54} - 1605 q^{55} - 1440 q^{56} - 1410 q^{57} + 1200 q^{58} + 1310 q^{59} + 1700 q^{60} + 315 q^{61} + 2590 q^{62} + 180 q^{63} + 695 q^{64} + 910 q^{65} + 1300 q^{66} + 840 q^{67} + 1350 q^{68} + 920 q^{69} + 140 q^{70} + 465 q^{71} + 175 q^{72} - 2555 q^{73} - 1470 q^{74} - 680 q^{75} + 190 q^{76} - 2235 q^{77} - 1780 q^{78} - 545 q^{79} - 3460 q^{80} - 1320 q^{81} - 2985 q^{82} + 520 q^{83} - 820 q^{84} + 2835 q^{85} + 905 q^{86} + 3510 q^{87} + 4675 q^{88} + 1940 q^{89} - 150 q^{90} + 1415 q^{91} - 2490 q^{92} - 2715 q^{93} - 290 q^{94} + 1635 q^{95} + 300 q^{96} + 850 q^{97} + 1870 q^{98} + 1615 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(11))$$

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
11.4.a $$\chi_{11}(1, \cdot)$$ 11.4.a.a 2 1
11.4.c $$\chi_{11}(3, \cdot)$$ 11.4.c.a 8 4