Properties

Label 4.4.10816.1-23.2-e
Base field \(\Q(\sqrt{2}, \sqrt{13})\)
Weight $[2, 2, 2, 2]$
Level norm $23$
Level $[23,23,-\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{3}{5}]$
Dimension $2$
CM no
Base change no

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Base field \(\Q(\sqrt{2}, \sqrt{13})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 9x^{2} + 10x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[23,23,-\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{3}{5}]$
Dimension: $2$
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:

\(x^{2} + x - 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{17}{5}w - \frac{9}{5}]$ $\phantom{-}e$
9 $[9, 3, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{22}{5}w - \frac{9}{5}]$ $-e$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{3}{5}w^{2} - \frac{22}{5}w + \frac{14}{5}]$ $-e$
17 $[17, 17, w + 1]$ $\phantom{-}e + 3$
17 $[17, 17, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{13}{5}]$ $-3$
17 $[17, 17, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{28}{5}]$ $\phantom{-}2e - 1$
17 $[17, 17, -w + 2]$ $-2e$
23 $[23, 23, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{6}{5}w - \frac{22}{5}]$ $-2e - 3$
23 $[23, 23, -\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{3}{5}]$ $\phantom{-}1$
23 $[23, 23, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{6}{5}w - \frac{12}{5}]$ $\phantom{-}2e + 1$
23 $[23, 23, -\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{13}{5}]$ $-6$
25 $[25, 5, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{33}{5}]$ $\phantom{-}e + 3$
25 $[25, 5, -w^{3} + w^{2} + 10w - 2]$ $-e - 4$
49 $[49, 7, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{34}{5}w - \frac{23}{5}]$ $-2e + 2$
49 $[49, 7, \frac{4}{5}w^{3} - \frac{6}{5}w^{2} - \frac{34}{5}w + \frac{13}{5}]$ $\phantom{-}2e - 4$
79 $[79, 79, \frac{3}{5}w^{3} - \frac{7}{5}w^{2} - \frac{28}{5}w + \frac{21}{5}]$ $\phantom{-}e + 10$
79 $[79, 79, \frac{1}{5}w^{3} + \frac{1}{5}w^{2} - \frac{16}{5}w - \frac{13}{5}]$ $\phantom{-}5e - 1$
79 $[79, 79, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{11}{5}w - \frac{27}{5}]$ $-11$
79 $[79, 79, \frac{3}{5}w^{3} - \frac{2}{5}w^{2} - \frac{33}{5}w + \frac{11}{5}]$ $\phantom{-}2e - 9$
103 $[103, 103, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{1}{5}w - \frac{17}{5}]$ $-5e - 6$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23,23,-\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{3}{5}]$ $-1$