Properties

Label 2.2.133.1-21.2-g
Base field \(\Q(\sqrt{133}) \)
Weight $[2, 2]$
Level norm $21$
Level $[21,21,-w + 4]$
Dimension $10$
CM no
Base change no

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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 $[3, 3, -w - 5]$ $\phantom{-}1$
4 $[4, 2, 2]$ $\phantom{-}\frac{1}{48}e^{9} - \frac{5}{12}e^{7} - \frac{1}{24}e^{6} + \frac{41}{16}e^{5} + \frac{7}{8}e^{4} - 5e^{3} - \frac{25}{6}e^{2} + \frac{3}{2}e + 3$
7 $[7, 7, 3w - 19]$ $\phantom{-}1$
11 $[11, 11, -2w - 11]$ $\phantom{-}\frac{1}{12}e^{7} - \frac{17}{12}e^{5} - \frac{1}{6}e^{4} + \frac{13}{2}e^{3} + 2e^{2} - 6e - \frac{2}{3}$
11 $[11, 11, -2w + 13]$ $-\frac{1}{2}e^{3} - \frac{1}{2}e^{2} + 4e + 2$
13 $[13, 13, w + 4]$ $-\frac{1}{24}e^{8} - \frac{1}{24}e^{7} + \frac{17}{24}e^{6} + \frac{19}{24}e^{5} - \frac{19}{6}e^{4} - \frac{19}{4}e^{3} + \frac{5}{2}e^{2} + \frac{22}{3}e + \frac{4}{3}$
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 $[23, 23, -w - 7]$ $\phantom{-}\frac{1}{24}e^{9} - \frac{1}{24}e^{8} - \frac{23}{24}e^{7} + \frac{5}{8}e^{6} + \frac{91}{12}e^{5} - \frac{7}{4}e^{4} - 24e^{3} - \frac{17}{6}e^{2} + \frac{64}{3}e + 2$
23 $[23, 23, w - 8]$ $-\frac{1}{24}e^{9} + \frac{11}{12}e^{7} + \frac{1}{12}e^{6} - \frac{157}{24}e^{5} - \frac{17}{12}e^{4} + \frac{33}{2}e^{3} + \frac{35}{6}e^{2} - 10e - \frac{8}{3}$
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 $[43, 43, -3w - 17]$ $\phantom{-}\frac{1}{24}e^{9} - \frac{1}{24}e^{8} - \frac{23}{24}e^{7} + \frac{5}{8}e^{6} + \frac{85}{12}e^{5} - \frac{7}{4}e^{4} - 18e^{3} - \frac{10}{3}e^{2} + \frac{28}{3}e + 2$
43 $[43, 43, -3w + 20]$ $\phantom{-}\frac{1}{24}e^{9} - \frac{1}{12}e^{8} - \frac{5}{6}e^{7} + \frac{19}{12}e^{6} + \frac{127}{24}e^{5} - 9e^{4} - \frac{25}{2}e^{3} + \frac{103}{6}e^{2} + \frac{23}{3}e - 8$
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 $[59, 59, 3w + 14]$ $-\frac{1}{48}e^{9} + \frac{7}{12}e^{7} + \frac{1}{24}e^{6} - \frac{259}{48}e^{5} - \frac{5}{24}e^{4} + \frac{35}{2}e^{3} - \frac{7}{3}e^{2} - \frac{23}{2}e + \frac{20}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3,3,w + 5]$ $-1$
$7$ $[7,7,-3w - 16]$ $-1$