Properties

Label 3.3.229.1-37.3-c
Base field 3.3.229.1
Weight $[2, 2, 2]$
Level norm $37$
Level $[37, 37, 2w^{2} - w - 10]$
Dimension $4$
CM no
Base change no

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Base field 3.3.229.1

Generator \(w\), with minimal polynomial \(x^{3} - 4x - 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[37, 37, 2w^{2} - w - 10]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 17x^{2} + 36\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w + 1]$ $-\frac{1}{6}e^{3} + \frac{11}{6}e$
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w^{2} - 2]$ $\phantom{-}0$
13 $[13, 13, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{6}e^{3} - \frac{17}{6}e$
23 $[23, 23, -2w + 1]$ $\phantom{-}e^{2} - 5$
27 $[27, 3, 3]$ $\phantom{-}4$
29 $[29, 29, -2w + 3]$ $-e^{2} + 11$
31 $[31, 31, -2w^{2} + 2w + 3]$ $-\frac{1}{6}e^{3} + \frac{5}{6}e$
37 $[37, 37, 4w^{2} - 2w - 13]$ $-2e$
37 $[37, 37, -2w^{2} + 5]$ $-2e$
37 $[37, 37, 2w^{2} - w - 10]$ $\phantom{-}1$
41 $[41, 41, w^{2} - 2w - 4]$ $-\frac{1}{3}e^{3} + \frac{11}{3}e$
47 $[47, 47, w - 4]$ $-e^{2} + 5$
49 $[49, 7, 2w^{2} - w - 4]$ $\phantom{-}\frac{1}{3}e^{3} - \frac{11}{3}e$
53 $[53, 53, 2w^{2} - 2w - 7]$ $-2e$
53 $[53, 53, 3w^{2} - 2w - 8]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{9}{2}e$
53 $[53, 53, 2w + 5]$ $-2$
59 $[59, 59, 2w^{2} - 2w - 9]$ $-\frac{1}{6}e^{3} + \frac{29}{6}e$
67 $[67, 67, 2w^{2} - 3]$ $-\frac{1}{6}e^{3} + \frac{29}{6}e$
73 $[73, 73, 2w^{2} + w - 8]$ $\phantom{-}2e^{2} - 16$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, 2w^{2} - w - 10]$ $-1$