Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 25
Level $[25, 5, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{12}{5}w + 1]$
Label 4.4.11525.1-25.2-a
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 $[25, 5, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{12}{5}w + 1]$
Label 4.4.11525.1-25.2-a
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 23

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 2x^{3} \) \(\mathstrut -\mathstrut 28x^{2} \) \(\mathstrut +\mathstrut 91x \) \(\mathstrut -\mathstrut 69\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}1$
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 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $-\frac{20}{37}e^{3} - \frac{4}{37}e^{2} + \frac{529}{37}e - \frac{708}{37}$
16 $[16, 2, 2]$ $-\frac{2}{37}e^{3} + \frac{7}{37}e^{2} + \frac{64}{37}e - \frac{241}{37}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $-\frac{32}{37}e^{3} + \frac{1}{37}e^{2} + \frac{876}{37}e - \frac{1303}{37}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}\frac{10}{37}e^{3} + \frac{2}{37}e^{2} - \frac{283}{37}e + \frac{428}{37}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{22}{37}e^{3} - \frac{3}{37}e^{2} - \frac{630}{37}e + \frac{875}{37}$
19 $[19, 19, w - 1]$ $\phantom{-}\frac{10}{37}e^{3} + \frac{2}{37}e^{2} - \frac{283}{37}e + \frac{206}{37}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{15}{37}e^{3} + \frac{3}{37}e^{2} - \frac{443}{37}e + \frac{531}{37}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}\frac{33}{37}e^{3} - \frac{23}{37}e^{2} - \frac{945}{37}e + \frac{1479}{37}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{13}{37}e^{3} - \frac{10}{37}e^{2} + \frac{342}{37}e - \frac{364}{37}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $-\frac{1}{37}e^{3} + \frac{22}{37}e^{2} + \frac{106}{37}e - \frac{472}{37}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}\frac{18}{37}e^{3} + \frac{11}{37}e^{2} - \frac{502}{37}e + \frac{356}{37}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $-\frac{22}{37}e^{3} + \frac{3}{37}e^{2} + \frac{630}{37}e - \frac{1060}{37}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $-\frac{13}{37}e^{3} - \frac{10}{37}e^{2} + \frac{379}{37}e - \frac{364}{37}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{21}{37}e^{3} + \frac{18}{37}e^{2} + \frac{635}{37}e - \frac{1180}{37}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $-\frac{15}{37}e^{3} + \frac{34}{37}e^{2} + \frac{443}{37}e - \frac{1197}{37}$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}\frac{61}{37}e^{3} - \frac{10}{37}e^{2} - \frac{1693}{37}e + \frac{2559}{37}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{25}{37}e^{3} - \frac{32}{37}e^{2} - \frac{763}{37}e + \frac{1403}{37}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-1$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $1$