Properties

Label 2.2.321.1-4.2-a
Base field \(\Q(\sqrt{321}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 4, w]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\sqrt{321}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 80\); narrow class number \(6\) and class number \(3\).

Form

Weight: $[2, 2]$
Level: $[4, 4, w]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $42$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 4x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
3 $[3, 3, -2w + 19]$ $\phantom{-}e^{2} - e - 3$
5 $[5, 5, w]$ $\phantom{-}e^{2} - e - 2$
5 $[5, 5, w + 4]$ $-e^{2} + e + 4$
13 $[13, 13, w + 1]$ $-2e + 1$
13 $[13, 13, w + 11]$ $\phantom{-}2e - 3$
17 $[17, 17, w + 3]$ $-e^{2} - e + 2$
17 $[17, 17, w + 13]$ $\phantom{-}e^{2} + e - 4$
19 $[19, 19, w + 6]$ $-3$
19 $[19, 19, w + 12]$ $\phantom{-}2e - 1$
37 $[37, 37, w + 2]$ $-2e - 5$
37 $[37, 37, w + 34]$ $\phantom{-}2e + 3$
49 $[49, 7, -7]$ $\phantom{-}2e^{2} - 2e - 6$
59 $[59, 59, -4w - 33]$ $-2e^{2} - 6e + 8$
59 $[59, 59, 4w - 37]$ $-4e^{2} + 4e + 14$
61 $[61, 61, w + 28]$ $-6e^{2} + 2e + 11$
61 $[61, 61, w + 32]$ $-2e^{2} + 2e + 11$
71 $[71, 71, w + 22]$ $-e^{2} - e - 8$
71 $[71, 71, w + 48]$ $\phantom{-}e^{2} - e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $-1$