Properties

Label 3.3.697.1-25.1-b
Base field 3.3.697.1
Weight $[2, 2, 2]$
Level norm $25$
Level $[25, 5, w^{2} - 7]$
Dimension $4$
CM no
Base change no

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Base field 3.3.697.1

Generator \(w\), with minimal polynomial \(x^{3} - 7x - 5\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[25, 5, w^{2} - 7]$
Dimension: $4$
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:

\(x^{4} - 19x^{2} - 9x + 34\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, w]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-\frac{1}{3}e^{2} + \frac{11}{3}$
11 $[11, 11, -w^{2} + 2w + 4]$ $\phantom{-}\frac{1}{3}e^{2} - e - \frac{11}{3}$
11 $[11, 11, -w + 2]$ $-\frac{2}{15}e^{3} + \frac{2}{15}e^{2} + \frac{16}{15}e - \frac{13}{15}$
11 $[11, 11, w - 1]$ $-\frac{1}{15}e^{3} - \frac{4}{15}e^{2} + \frac{23}{15}e + \frac{26}{15}$
13 $[13, 13, -w^{2} + w + 4]$ $\phantom{-}\frac{1}{15}e^{3} + \frac{4}{15}e^{2} - \frac{23}{15}e - \frac{86}{15}$
17 $[17, 17, -w^{2} + w + 8]$ $\phantom{-}e + 1$
17 $[17, 17, -w^{2} + w + 3]$ $-\frac{1}{15}e^{3} + \frac{11}{15}e^{2} + \frac{8}{15}e - \frac{94}{15}$
19 $[19, 19, -w^{2} + 6]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{8}{15}e^{2} - \frac{18}{5}e + \frac{22}{15}$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{1}{5}e^{2} - \frac{18}{5}e - \frac{26}{5}$
25 $[25, 5, w^{2} - 7]$ $-1$
27 $[27, 3, -3]$ $-e - 3$
31 $[31, 31, w^{2} - 2w - 8]$ $-\frac{1}{5}e^{3} - \frac{2}{15}e^{2} + \frac{18}{5}e - \frac{32}{15}$
37 $[37, 37, w^{2} - 2w - 6]$ $\phantom{-}\frac{1}{5}e^{3} - \frac{13}{15}e^{2} - \frac{13}{5}e + \frac{62}{15}$
41 $[41, 41, -w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{1}{3}e^{2} - \frac{17}{3}e - \frac{4}{3}$
41 $[41, 41, w^{2} - 2w - 7]$ $\phantom{-}\frac{1}{3}e^{2} + \frac{7}{3}$
47 $[47, 47, 2w^{2} - 3w - 7]$ $-\frac{4}{15}e^{3} - \frac{2}{5}e^{2} + \frac{62}{15}e + \frac{13}{5}$
53 $[53, 53, -w^{2} + w + 9]$ $\phantom{-}\frac{4}{15}e^{3} - \frac{4}{15}e^{2} - \frac{47}{15}e + \frac{86}{15}$
61 $[61, 61, 3w^{2} - 2w - 17]$ $\phantom{-}\frac{1}{3}e^{2} - e + \frac{4}{3}$
67 $[67, 67, 2w - 1]$ $\phantom{-}\frac{7}{15}e^{3} - \frac{7}{15}e^{2} - \frac{116}{15}e - \frac{52}{15}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$25$ $[25, 5, w^{2} - 7]$ $1$