Base field \(\Q(\sqrt{133}) \)
Generator \(w\), with minimal polynomial \(x^{2} - x - 33\); narrow class number \(2\) and class number \(1\).
Form
Weight: | $[2, 2]$ |
Level: | $[21,21,-w + 4]$ |
Dimension: | $10$ |
CM: | no |
Base change: | no |
Newspace dimension: | $34$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{10} + 2x^{9} - 22x^{8} - 40x^{7} + 161x^{6} + 246x^{5} - 460x^{4} - 520x^{3} + 424x^{2} + 320x - 64\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
3 | $[3, 3, -w + 6]$ | $\phantom{-}e$ |
3 | $[3, 3, -w - 5]$ | $-1$ |
4 | $[4, 2, 2]$ | $-\frac{1}{48}e^{9} + \frac{5}{12}e^{7} - \frac{1}{24}e^{6} - \frac{41}{16}e^{5} + \frac{7}{8}e^{4} + 5e^{3} - \frac{25}{6}e^{2} - \frac{3}{2}e + 3$ |
7 | $[7, 7, 3w - 19]$ | $\phantom{-}1$ |
11 | $[11, 11, -2w - 11]$ | $-\frac{1}{12}e^{7} + \frac{17}{12}e^{5} - \frac{1}{6}e^{4} - \frac{13}{2}e^{3} + 2e^{2} + 6e - \frac{2}{3}$ |
11 | $[11, 11, -2w + 13]$ | $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - 4e + 2$ |
13 | $[13, 13, w + 4]$ | $\phantom{-}\frac{1}{24}e^{8} - \frac{1}{24}e^{7} - \frac{17}{24}e^{6} + \frac{19}{24}e^{5} + \frac{19}{6}e^{4} - \frac{19}{4}e^{3} - \frac{5}{2}e^{2} + \frac{22}{3}e - \frac{4}{3}$ |
13 | $[13, 13, -w + 5]$ | $-\frac{1}{48}e^{9} - \frac{1}{12}e^{8} + \frac{1}{3}e^{7} + \frac{13}{8}e^{6} - \frac{17}{16}e^{5} - \frac{229}{24}e^{4} - \frac{9}{4}e^{3} + \frac{107}{6}e^{2} + \frac{41}{6}e - \frac{20}{3}$ |
19 | $[19, 19, 5w - 31]$ | $\phantom{-}\frac{1}{16}e^{9} + \frac{1}{8}e^{8} - \frac{31}{24}e^{7} - \frac{9}{4}e^{6} + \frac{403}{48}e^{5} + \frac{271}{24}e^{4} - 19e^{3} - \frac{31}{2}e^{2} + \frac{19}{2}e + \frac{14}{3}$ |
23 | $[23, 23, -w - 7]$ | $-\frac{1}{24}e^{9} - \frac{1}{24}e^{8} + \frac{23}{24}e^{7} + \frac{5}{8}e^{6} - \frac{91}{12}e^{5} - \frac{7}{4}e^{4} + 24e^{3} - \frac{17}{6}e^{2} - \frac{64}{3}e + 2$ |
23 | $[23, 23, w - 8]$ | $\phantom{-}\frac{1}{24}e^{9} - \frac{11}{12}e^{7} + \frac{1}{12}e^{6} + \frac{157}{24}e^{5} - \frac{17}{12}e^{4} - \frac{33}{2}e^{3} + \frac{35}{6}e^{2} + 10e - \frac{8}{3}$ |
25 | $[25, 5, -5]$ | $\phantom{-}\frac{1}{24}e^{8} + \frac{1}{24}e^{7} - \frac{17}{24}e^{6} - \frac{7}{8}e^{5} + \frac{10}{3}e^{4} + 5e^{3} - \frac{9}{2}e^{2} - \frac{23}{3}e + \frac{4}{3}$ |
31 | $[31, 31, -w - 1]$ | $-\frac{1}{48}e^{9} + \frac{1}{24}e^{8} + \frac{11}{24}e^{7} - \frac{3}{4}e^{6} - \frac{55}{16}e^{5} + \frac{89}{24}e^{4} + \frac{21}{2}e^{3} - \frac{8}{3}e^{2} - \frac{73}{6}e - \frac{20}{3}$ |
31 | $[31, 31, w - 2]$ | $-\frac{1}{48}e^{9} + \frac{7}{12}e^{7} - \frac{1}{24}e^{6} - \frac{259}{48}e^{5} + \frac{17}{24}e^{4} + 18e^{3} - \frac{8}{3}e^{2} - \frac{27}{2}e - \frac{8}{3}$ |
41 | $[41, 41, 6w + 31]$ | $-\frac{1}{24}e^{9} + \frac{13}{12}e^{7} - \frac{1}{12}e^{6} - \frac{77}{8}e^{5} + \frac{7}{4}e^{4} + \frac{129}{4}e^{3} - \frac{28}{3}e^{2} - 27e + 4$ |
41 | $[41, 41, 6w - 37]$ | $-\frac{1}{48}e^{9} - \frac{1}{12}e^{8} + \frac{1}{2}e^{7} + \frac{13}{8}e^{6} - \frac{187}{48}e^{5} - \frac{233}{24}e^{4} + \frac{45}{4}e^{3} + \frac{107}{6}e^{2} - \frac{67}{6}e - \frac{16}{3}$ |
43 | $[43, 43, -3w - 17]$ | $-\frac{1}{24}e^{9} - \frac{1}{24}e^{8} + \frac{23}{24}e^{7} + \frac{5}{8}e^{6} - \frac{85}{12}e^{5} - \frac{7}{4}e^{4} + 18e^{3} - \frac{10}{3}e^{2} - \frac{28}{3}e + 2$ |
43 | $[43, 43, -3w + 20]$ | $-\frac{1}{24}e^{9} - \frac{1}{12}e^{8} + \frac{5}{6}e^{7} + \frac{19}{12}e^{6} - \frac{127}{24}e^{5} - 9e^{4} + \frac{25}{2}e^{3} + \frac{103}{6}e^{2} - \frac{23}{3}e - 8$ |
59 | $[59, 59, 3w - 17]$ | $\phantom{-}\frac{1}{16}e^{9} + \frac{1}{8}e^{8} - \frac{35}{24}e^{7} - \frac{9}{4}e^{6} + \frac{539}{48}e^{5} + \frac{263}{24}e^{4} - 32e^{3} - \frac{21}{2}e^{2} + \frac{45}{2}e - \frac{14}{3}$ |
59 | $[59, 59, 3w + 14]$ | $-\frac{1}{48}e^{9} + \frac{7}{12}e^{7} - \frac{1}{24}e^{6} - \frac{259}{48}e^{5} + \frac{5}{24}e^{4} + \frac{35}{2}e^{3} + \frac{7}{3}e^{2} - \frac{23}{2}e - \frac{20}{3}$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$3$ | $[3,3,w + 5]$ | $1$ |
$7$ | $[7,7,-3w - 16]$ | $-1$ |