Properties

Label 4.4.10816.1-16.1-c
Base field \(\Q(\sqrt{2}, \sqrt{13})\)
Weight $[2, 2, 2, 2]$
Level norm $16$
Level $[16, 2, 2]$
Dimension $4$
CM no
Base change yes

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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: $[16, 2, 2]$
Dimension: $4$
CM: no
Base change: yes
Newspace dimension: $12$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 8x^{3} - 10x^{2} + 152x - 119\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{17}{5}w - \frac{9}{5}]$ $\phantom{-}0$
9 $[9, 3, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{22}{5}w - \frac{9}{5}]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{25}{4}e + \frac{47}{4}$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{3}{5}w^{2} - \frac{22}{5}w + \frac{14}{5}]$ $\phantom{-}e$
17 $[17, 17, w + 1]$ $-\frac{3}{8}e^{3} + \frac{5}{8}e^{2} + \frac{71}{8}e - \frac{9}{8}$
17 $[17, 17, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{13}{5}]$ $-\frac{3}{8}e^{3} + \frac{5}{8}e^{2} + \frac{71}{8}e - \frac{9}{8}$
17 $[17, 17, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{28}{5}]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{1}{8}e^{2} - \frac{29}{8}e - \frac{21}{8}$
17 $[17, 17, -w + 2]$ $\phantom{-}\frac{1}{8}e^{3} + \frac{1}{8}e^{2} - \frac{29}{8}e - \frac{21}{8}$
23 $[23, 23, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{6}{5}w - \frac{22}{5}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{23}{2}e + \frac{37}{2}$
23 $[23, 23, -\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{3}{5}]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{17}{4}e + \frac{27}{4}$
23 $[23, 23, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{6}{5}w - \frac{12}{5}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{23}{2}e + \frac{37}{2}$
23 $[23, 23, -\frac{1}{5}w^{3} - \frac{1}{5}w^{2} + \frac{11}{5}w + \frac{13}{5}]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{3}{4}e^{2} - \frac{17}{4}e + \frac{27}{4}$
25 $[25, 5, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{39}{5}w - \frac{33}{5}]$ $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{21}{4}e - \frac{27}{4}$
25 $[25, 5, -w^{3} + w^{2} + 10w - 2]$ $-\frac{1}{4}e^{3} + \frac{3}{4}e^{2} + \frac{21}{4}e - \frac{27}{4}$
49 $[49, 7, -\frac{4}{5}w^{3} + \frac{6}{5}w^{2} + \frac{34}{5}w - \frac{23}{5}]$ $-\frac{1}{8}e^{3} + \frac{3}{8}e^{2} + \frac{21}{8}e - \frac{87}{8}$
49 $[49, 7, \frac{4}{5}w^{3} - \frac{6}{5}w^{2} - \frac{34}{5}w + \frac{13}{5}]$ $-\frac{1}{8}e^{3} + \frac{3}{8}e^{2} + \frac{21}{8}e - \frac{87}{8}$
79 $[79, 79, \frac{3}{5}w^{3} - \frac{7}{5}w^{2} - \frac{28}{5}w + \frac{21}{5}]$ $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{29}{4}e - \frac{21}{4}$
79 $[79, 79, \frac{1}{5}w^{3} + \frac{1}{5}w^{2} - \frac{16}{5}w - \frac{13}{5}]$ $-\frac{1}{4}e^{3} + \frac{1}{4}e^{2} + \frac{29}{4}e - \frac{21}{4}$
79 $[79, 79, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{11}{5}w - \frac{27}{5}]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{25}{2}e + 5$
79 $[79, 79, \frac{3}{5}w^{3} - \frac{2}{5}w^{2} - \frac{33}{5}w + \frac{11}{5}]$ $\phantom{-}\frac{1}{2}e^{3} - e^{2} - \frac{25}{2}e + 5$
103 $[103, 103, -\frac{1}{5}w^{3} + \frac{4}{5}w^{2} + \frac{1}{5}w - \frac{17}{5}]$ $-\frac{3}{4}e^{3} + \frac{7}{4}e^{2} + \frac{71}{4}e - \frac{99}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$4$ $[4, 2, -\frac{2}{5}w^{3} + \frac{3}{5}w^{2} + \frac{17}{5}w - \frac{9}{5}]$ $1$