Properties

Label 4.4.4225.1-36.3-d
Base field \(\Q(\sqrt{5}, \sqrt{13})\)
Weight $[2, 2, 2, 2]$
Level norm $36$
Level $[36,6,\frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{9}{4}w + \frac{1}{2}]$
Dimension $3$
CM no
Base change no

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Base field \(\Q(\sqrt{5}, \sqrt{13})\)

Generator \(w\), with minimal polynomial \(x^{4} - 9x^{2} + 4\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[36,6,\frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{9}{4}w + \frac{1}{2}]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $7$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - x^{2} - 7x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, w]$ $\phantom{-}e$
4 $[4, 2, -\frac{1}{2}w^{3} + \frac{9}{2}w]$ $\phantom{-}1$
9 $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w - \frac{1}{2}]$ $\phantom{-}1$
9 $[9, 3, \frac{1}{4}w^{3} - \frac{11}{4}w + \frac{1}{2}]$ $\phantom{-}e^{2} - 2e - 5$
25 $[25, 5, \frac{1}{2}w^{3} - \frac{7}{2}w]$ $-e - 1$
29 $[29, 29, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{9}{4}w - \frac{1}{2}]$ $\phantom{-}2e^{2} - 2e - 10$
29 $[29, 29, -\frac{1}{2}w^{2} - \frac{1}{2}w + 4]$ $-2e^{2} + 2e + 6$
29 $[29, 29, -\frac{1}{2}w^{2} + \frac{1}{2}w + 4]$ $-e + 3$
29 $[29, 29, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{9}{4}w + \frac{1}{2}]$ $-e^{2} + 3e + 8$
49 $[49, 7, \frac{3}{4}w^{3} + \frac{1}{2}w^{2} - \frac{23}{4}w - \frac{3}{2}]$ $\phantom{-}3e + 3$
49 $[49, 7, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 3w - 3]$ $-e^{2} + 11$
61 $[61, 61, \frac{1}{2}w^{3} + \frac{1}{2}w^{2} - 5w - 1]$ $-2$
61 $[61, 61, -\frac{1}{4}w^{3} - \frac{1}{2}w^{2} + \frac{13}{4}w + \frac{7}{2}]$ $-2e^{2} + e + 11$
61 $[61, 61, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} + \frac{13}{4}w - \frac{7}{2}]$ $-e^{2} + 4e + 3$
61 $[61, 61, -\frac{1}{2}w^{3} + \frac{1}{2}w^{2} + 5w - 1]$ $-2$
79 $[79, 79, \frac{3}{4}w^{3} - \frac{25}{4}w - \frac{9}{2}]$ $-2e^{2} - 2e + 12$
79 $[79, 79, -\frac{1}{4}w^{3} + \frac{1}{2}w^{2} - \frac{3}{4}w - \frac{3}{2}]$ $-3e^{2} + 2e + 17$
79 $[79, 79, \frac{1}{4}w^{3} - \frac{3}{4}w - \frac{9}{2}]$ $-3e - 1$
79 $[79, 79, \frac{3}{2}w^{3} + \frac{1}{2}w^{2} - 13w - 3]$ $\phantom{-}2e^{2} + e - 7$
101 $[101, 101, \frac{1}{4}w^{3} + w^{2} - \frac{7}{4}w - \frac{5}{2}]$ $\phantom{-}2e^{2} - 7e - 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4,2,-\frac{1}{2}w^{3} + \frac{9}{2}w]$ $-1$
$9$ $[9,3,\frac{1}{4}w^{3} - \frac{11}{4}w - \frac{1}{2}]$ $-1$