Properties

Label 4.4.13525.1-11.1-c
Base field 4.4.13525.1
Weight $[2, 2, 2, 2]$
Level norm $11$
Level $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$
Dimension $4$
CM no
Base change no

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Base field 4.4.13525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 12x^{2} + 8x + 29\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $10$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 2x^{3} - 6x^{2} + 2x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -w + 2]$ $\phantom{-}e$
5 $[5, 5, -\frac{3}{5}w^{3} - w^{2} + \frac{26}{5}w + \frac{42}{5}]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{3}{2}e - \frac{5}{2}$
9 $[9, 3, \frac{2}{5}w^{3} - \frac{19}{5}w - \frac{3}{5}]$ $\phantom{-}0$
9 $[9, 3, -\frac{1}{5}w^{3} + \frac{2}{5}w + \frac{4}{5}]$ $-\frac{1}{2}e^{3} + \frac{3}{2}e^{2} + \frac{1}{2}e - \frac{5}{2}$
11 $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $\phantom{-}1$
11 $[11, 11, \frac{1}{5}w^{3} - w^{2} - \frac{7}{5}w + \frac{36}{5}]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{3}{2}e^{2} - \frac{3}{2}e + \frac{3}{2}$
16 $[16, 2, 2]$ $-\frac{1}{2}e^{3} + \frac{1}{2}e^{2} + \frac{9}{2}e - \frac{3}{2}$
29 $[29, 29, -w]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{11}{2}e^{2} - \frac{27}{2}e + \frac{1}{2}$
29 $[29, 29, \frac{1}{5}w^{3} - \frac{12}{5}w + \frac{1}{5}]$ $-3e^{3} + 5e^{2} + 19e - 5$
41 $[41, 41, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{38}{5}]$ $-2e^{3} + 3e^{2} + 11e - 1$
41 $[41, 41, -w^{2} + 10]$ $\phantom{-}e^{3} - 3e^{2} - 5e + 1$
41 $[41, 41, \frac{11}{5}w^{3} + 3w^{2} - \frac{102}{5}w - \frac{149}{5}]$ $\phantom{-}2e^{3} - 5e^{2} - 11e + 9$
41 $[41, 41, -\frac{1}{5}w^{3} + w^{2} + \frac{7}{5}w - \frac{26}{5}]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{1}{2}e^{2} - \frac{13}{2}e - \frac{3}{2}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{19}{5}]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{9}{2}e^{2} - \frac{27}{2}e - \frac{1}{2}$
49 $[49, 7, \frac{1}{5}w^{3} + w^{2} - \frac{12}{5}w - \frac{44}{5}]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{13}{2}e^{2} - \frac{17}{2}e + \frac{15}{2}$
59 $[59, 59, -\frac{4}{5}w^{3} - w^{2} + \frac{33}{5}w + \frac{36}{5}]$ $\phantom{-}3e^{3} - 7e^{2} - 15e + 5$
59 $[59, 59, -2w^{3} - 3w^{2} + 17w + 26]$ $-\frac{1}{2}e^{3} + \frac{9}{2}e^{2} - \frac{9}{2}e - \frac{23}{2}$
61 $[61, 61, -\frac{1}{5}w^{3} + w^{2} + \frac{12}{5}w - \frac{51}{5}]$ $-3e^{3} + 6e^{2} + 19e - 4$
61 $[61, 61, \frac{4}{5}w^{3} + w^{2} - \frac{28}{5}w - \frac{41}{5}]$ $\phantom{-}\frac{5}{2}e^{3} - \frac{9}{2}e^{2} - \frac{27}{2}e + \frac{3}{2}$
71 $[71, 71, \frac{1}{5}w^{3} + w^{2} - \frac{7}{5}w - \frac{49}{5}]$ $\phantom{-}2e^{3} - 6e^{2} - 10e + 7$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$11$ $[11, 11, -\frac{2}{5}w^{3} - w^{2} + \frac{14}{5}w + \frac{28}{5}]$ $-1$