# Properties

 Label 11.2 Level 11 Weight 2 Dimension 1 Nonzero newspaces 1 Newform subspaces 1 Sturm bound 20 Trace bound 0

## Defining parameters

 Level: $$N$$ = $$11\( 11$$ \) Weight: $$k$$ = $$2$$ Nonzero newspaces: $$1$$ Newform subspaces: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(11))$$.

Total New Old
Modular forms 10 10 0
Cusp forms 1 1 0
Eisenstein series 9 9 0

## Trace form

 $$q - 2q^{2} - q^{3} + 2q^{4} + q^{5} + 2q^{6} - 2q^{7} - 2q^{9} + O(q^{10})$$ $$q - 2q^{2} - q^{3} + 2q^{4} + q^{5} + 2q^{6} - 2q^{7} - 2q^{9} - 2q^{10} + q^{11} - 2q^{12} + 4q^{13} + 4q^{14} - q^{15} - 4q^{16} - 2q^{17} + 4q^{18} + 2q^{20} + 2q^{21} - 2q^{22} - q^{23} - 4q^{25} - 8q^{26} + 5q^{27} - 4q^{28} + 2q^{30} + 7q^{31} + 8q^{32} - q^{33} + 4q^{34} - 2q^{35} - 4q^{36} + 3q^{37} - 4q^{39} - 8q^{41} - 4q^{42} - 6q^{43} + 2q^{44} - 2q^{45} + 2q^{46} + 8q^{47} + 4q^{48} - 3q^{49} + 8q^{50} + 2q^{51} + 8q^{52} - 6q^{53} - 10q^{54} + q^{55} + 5q^{59} - 2q^{60} + 12q^{61} - 14q^{62} + 4q^{63} - 8q^{64} + 4q^{65} + 2q^{66} - 7q^{67} - 4q^{68} + q^{69} + 4q^{70} - 3q^{71} + 4q^{73} - 6q^{74} + 4q^{75} - 2q^{77} + 8q^{78} - 10q^{79} - 4q^{80} + q^{81} + 16q^{82} - 6q^{83} + 4q^{84} - 2q^{85} + 12q^{86} + 15q^{89} + 4q^{90} - 8q^{91} - 2q^{92} - 7q^{93} - 16q^{94} - 8q^{96} - 7q^{97} + 6q^{98} - 2q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$

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
11.2.a $$\chi_{11}(1, \cdot)$$ 11.2.a.a 1 1
11.2.c $$\chi_{11}(3, \cdot)$$ None 0 4

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 2 T + 2 T^{2}$$
$3$ $$1 + T + 3 T^{2}$$
$5$ $$1 - T + 5 T^{2}$$
$7$ $$1 + 2 T + 7 T^{2}$$
$11$ $$1 - T$$
$13$ $$1 - 4 T + 13 T^{2}$$
$17$ $$1 + 2 T + 17 T^{2}$$
$19$ $$1 + 19 T^{2}$$
$23$ $$1 + T + 23 T^{2}$$
$29$ $$1 + 29 T^{2}$$
$31$ $$1 - 7 T + 31 T^{2}$$
$37$ $$1 - 3 T + 37 T^{2}$$
$41$ $$1 + 8 T + 41 T^{2}$$
$43$ $$1 + 6 T + 43 T^{2}$$
$47$ $$1 - 8 T + 47 T^{2}$$
$53$ $$1 + 6 T + 53 T^{2}$$
$59$ $$1 - 5 T + 59 T^{2}$$
$61$ $$1 - 12 T + 61 T^{2}$$
$67$ $$1 + 7 T + 67 T^{2}$$
$71$ $$1 + 3 T + 71 T^{2}$$
$73$ $$1 - 4 T + 73 T^{2}$$
$79$ $$1 + 10 T + 79 T^{2}$$
$83$ $$1 + 6 T + 83 T^{2}$$
$89$ $$1 - 15 T + 89 T^{2}$$
$97$ $$1 + 7 T + 97 T^{2}$$