Properties

Label 3.3.1957.1-2.1-f
Base field 3.3.1957.1
Weight $[2, 2, 2]$
Level norm $2$
Level $[2, 2, w^{2}]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1957.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 9x + 10\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2, 2]$
Level: $[2, 2, w^{2}]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $16$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{6} + 19x^{4} + 75x^{2} + 9\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w^{2}]$ $\phantom{-}\frac{1}{36}e^{5} + \frac{11}{18}e^{3} + \frac{35}{12}e$
4 $[4, 2, w^{2} + w + 1]$ $\phantom{-}e$
5 $[5, 5, w]$ $\phantom{-}\frac{1}{12}e^{5} + \frac{4}{3}e^{3} + \frac{13}{4}e$
11 $[11, 11, 10w + 4]$ $-\frac{1}{4}e^{5} - \frac{9}{2}e^{3} - \frac{65}{4}e$
13 $[13, 13, 12w^{2} + w + 7]$ $-\frac{1}{4}e^{5} - \frac{9}{2}e^{3} - \frac{65}{4}e$
17 $[17, 17, w + 1]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{9}{2}$
17 $[17, 17, 16w^{2} + 16]$ $\phantom{-}\frac{1}{12}e^{5} + \frac{11}{6}e^{3} + \frac{31}{4}e$
17 $[17, 17, 16w^{2} + 16w + 8]$ $\phantom{-}\frac{1}{6}e^{5} + \frac{19}{6}e^{3} + 13e$
19 $[19, 19, 18w^{2} + 18w + 1]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{19}{3}e^{3} + 24e$
19 $[19, 19, -w^{2} + 7]$ $-\frac{1}{4}e^{4} - \frac{7}{2}e^{2} - \frac{13}{4}$
25 $[25, 5, 4w^{2} + w + 4]$ $\phantom{-}\frac{1}{4}e^{5} + 5e^{3} + \frac{83}{4}e$
27 $[27, 3, -3]$ $-\frac{1}{4}e^{4} - \frac{7}{2}e^{2} - \frac{29}{4}$
29 $[29, 29, w + 7]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{13}{2}e$
41 $[41, 41, 40w^{2} + 18]$ $-2e$
43 $[43, 43, w^{2} - 11]$ $-8$
47 $[47, 47, 2w^{2} + 2w - 13]$ $\phantom{-}e^{2} + 3$
59 $[59, 59, w^{2} - 3]$ $\phantom{-}\frac{1}{4}e^{4} + \frac{5}{2}e^{2} + \frac{9}{4}$
73 $[73, 73, w^{2} + 2w - 1]$ $\phantom{-}\frac{1}{4}e^{4} + 5e^{2} + \frac{67}{4}$
79 $[79, 79, w^{2} + 37]$ $-\frac{5}{12}e^{5} - \frac{49}{6}e^{3} - \frac{127}{4}e$
97 $[97, 97, w^{2} + 2w - 7]$ $\phantom{-}\frac{1}{4}e^{4} + 4e^{2} + \frac{7}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w^{2}]$ $-\frac{1}{36}e^{5} - \frac{11}{18}e^{3} - \frac{35}{12}e$