Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 5, w]$
Label 4.4.11525.1-25.1-e
Dimension 6
CM no
Base change no

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Base field 4.4.11525.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 11x^{2} + 5x + 25\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[25, 5, w]$
Label 4.4.11525.1-25.1-e
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 20

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut -\mathstrut 34x^{4} \) \(\mathstrut +\mathstrut 26x^{2} \) \(\mathstrut -\mathstrut 5\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}0$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $-1$
11 $[11, 11, w + 1]$ $\phantom{-}e$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}3e^{5} - 101e^{3} + 44e$
16 $[16, 2, 2]$ $-5e^{5} + 168e^{3} - 64e$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-8e^{5} + 269e^{3} - 107e$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}2e^{4} - 67e^{2} + 20$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $-5e^{4} + 168e^{2} - 65$
19 $[19, 19, w - 1]$ $\phantom{-}5e^{5} - 168e^{3} + 64e$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}3e^{4} - 101e^{2} + 40$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}5e^{5} - 168e^{3} + 61e$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-2e^{5} + 67e^{3} - 18e$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $-e^{5} + 34e^{3} - 25e$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}6e^{5} - 202e^{3} + 90e$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}4e^{5} - 134e^{3} + 36e$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $-8e^{4} + 269e^{2} - 107$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}12e^{4} - 403e^{2} + 153$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $-2$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}3e^{4} - 101e^{2} + 33$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $-3e^{4} + 100e^{2} - 25$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-1$