Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25,5,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 1]$
Label 4.4.11525.1-25.3-b
Dimension 4
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 $[25,5,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 1]$
Label 4.4.11525.1-25.3-b
Dimension 4
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:
\(x^{4} \) \(\mathstrut -\mathstrut 2x^{3} \) \(\mathstrut -\mathstrut 10x^{2} \) \(\mathstrut +\mathstrut 15x \) \(\mathstrut -\mathstrut 3\)

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Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $\phantom{-}0$
11 $[11, 11, w + 1]$ $-\frac{2}{5}e^{3} + \frac{1}{5}e^{2} + \frac{19}{5}e + \frac{6}{5}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}\frac{3}{5}e^{3} - \frac{4}{5}e^{2} - \frac{31}{5}e + \frac{36}{5}$
16 $[16, 2, 2]$ $-\frac{2}{5}e^{3} + \frac{6}{5}e^{2} + \frac{24}{5}e - \frac{34}{5}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}\frac{6}{5}e^{3} - \frac{8}{5}e^{2} - \frac{67}{5}e + \frac{52}{5}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{31}{5}e - \frac{1}{5}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{3}{5}e^{3} - \frac{4}{5}e^{2} - \frac{26}{5}e + \frac{26}{5}$
19 $[19, 19, w - 1]$ $-\frac{3}{5}e^{3} + \frac{4}{5}e^{2} + \frac{31}{5}e - \frac{26}{5}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{8}{5}e^{3} - \frac{9}{5}e^{2} - \frac{96}{5}e + \frac{66}{5}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $-\frac{3}{5}e^{3} - \frac{1}{5}e^{2} + \frac{31}{5}e + \frac{24}{5}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{2}{5}e^{3} + \frac{6}{5}e^{2} + \frac{14}{5}e - \frac{34}{5}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $\phantom{-}\frac{2}{5}e^{3} - \frac{6}{5}e^{2} - \frac{14}{5}e + \frac{29}{5}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-\frac{4}{5}e^{3} + \frac{2}{5}e^{2} + \frac{63}{5}e - \frac{13}{5}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $-\frac{3}{5}e^{3} + \frac{9}{5}e^{2} + \frac{16}{5}e - \frac{46}{5}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}2e^{3} - 2e^{2} - 21e + 14$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{11}{5}e^{3} + \frac{13}{5}e^{2} + \frac{102}{5}e - \frac{47}{5}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{12}{5}e^{3} - \frac{16}{5}e^{2} - \frac{139}{5}e + \frac{99}{5}$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}e^{3} - e^{2} - 10e$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $-\frac{1}{5}e^{3} - \frac{2}{5}e^{2} + \frac{32}{5}e + \frac{38}{5}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5,5,\frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $1$