# Properties

 Label 11.5 Level 11 Weight 5 Dimension 15 Nonzero newspaces 2 Newform subspaces 3 Sturm bound 50 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$11$$ Weight: $$k$$ = $$5$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$50$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(\Gamma_1(11))$$.

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

## Trace form

 $$15q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} + 75q^{6} - 80q^{7} - 245q^{8} - 175q^{9} + O(q^{10})$$ $$15q - 5q^{2} - 5q^{3} - 5q^{4} - 5q^{5} + 75q^{6} - 80q^{7} - 245q^{8} - 175q^{9} + 100q^{11} + 790q^{12} + 250q^{13} + 1210q^{14} + 605q^{15} - 945q^{16} - 1250q^{17} - 3150q^{18} - 1025q^{19} - 900q^{20} + 1285q^{22} + 2405q^{23} + 5345q^{24} + 2645q^{25} + 1450q^{26} - 560q^{27} - 3580q^{28} - 2690q^{29} - 6740q^{30} - 4415q^{31} + 6720q^{33} + 4890q^{34} + 3610q^{35} + 990q^{36} - 2115q^{37} + 820q^{38} - 6880q^{39} - 2340q^{40} - 4550q^{41} - 490q^{42} - 4640q^{44} + 2240q^{45} + 4150q^{46} + 1510q^{47} + 3840q^{48} + 2030q^{49} + 8895q^{50} + 13155q^{51} + 14070q^{52} + 8740q^{53} - 7985q^{55} - 20140q^{56} - 26925q^{57} - 10940q^{58} - 10250q^{59} - 9740q^{60} + 9460q^{61} - 6200q^{62} + 9150q^{63} + 7495q^{64} - 7170q^{66} - 1205q^{67} - 9400q^{68} - 9515q^{69} + 9220q^{70} + 31975q^{71} + 43045q^{72} + 27950q^{73} + 43270q^{74} + 8655q^{75} - 9110q^{77} - 36800q^{78} - 41540q^{79} - 32460q^{80} - 15115q^{81} - 39815q^{82} - 18665q^{83} + 26250q^{84} - 4230q^{85} + 3075q^{86} - 12485q^{88} - 10225q^{89} + 18400q^{90} + 27790q^{91} - 1180q^{92} + 41205q^{93} + 18920q^{94} + 14110q^{95} - 21140q^{96} + 19470q^{97} - 8725q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(\Gamma_1(11))$$

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
11.5.b $$\chi_{11}(10, \cdot)$$ 11.5.b.a 1 1
11.5.b.b 2
11.5.d $$\chi_{11}(2, \cdot)$$ 11.5.d.a 12 4