Properties

Label 3.3.1765.1-5.2-a
Base field 3.3.1765.1
Weight $[2, 2, 2]$
Level norm $5$
Level $[5, 5, w - 1]$
Dimension $4$
CM no
Base change no

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Base field 3.3.1765.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 11x + 16\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[5, 5, w - 1]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 9x^{2} + 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 2]$ $\phantom{-}e$
4 $[4, 2, -w^{2} - w + 9]$ $-\frac{1}{2}e^{3} + \frac{7}{2}e$
5 $[5, 5, -2w^{2} - w + 21]$ $-e^{2} + 3$
5 $[5, 5, w - 1]$ $\phantom{-}1$
13 $[13, 13, -2w^{2} - w + 19]$ $-2e$
13 $[13, 13, w^{2} - 9]$ $-2$
13 $[13, 13, 3w^{2} + 2w - 29]$ $\phantom{-}2e$
17 $[17, 17, -w^{2} - 2w + 7]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e$
23 $[23, 23, -w^{2} + 3]$ $-\frac{1}{2}e^{3} + \frac{5}{2}e$
27 $[27, 3, -3]$ $\phantom{-}4$
31 $[31, 31, -w^{2} + 7]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e$
43 $[43, 43, w^{2} - 13]$ $\phantom{-}3e^{2} - 11$
47 $[47, 47, 2w^{2} + 3w - 11]$ $-e^{3} + 5e$
59 $[59, 59, w^{2} - 5]$ $\phantom{-}e^{3} - 5e$
61 $[61, 61, 5w^{2} + 4w - 47]$ $\phantom{-}2e^{3} - 12e$
61 $[61, 61, 4w - 7]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e$
61 $[61, 61, w - 5]$ $-2$
71 $[71, 71, -2w^{2} - 2w + 21]$ $-\frac{1}{2}e^{3} + \frac{5}{2}e$
73 $[73, 73, -2w^{2} + 4w - 1]$ $\phantom{-}e^{3} - 11e$
79 $[79, 79, w + 5]$ $\phantom{-}4e^{2} - 20$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$5$ $[5, 5, w - 1]$ $-1$