## 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

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

## 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 the 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