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-d
Dimension 8
CM no
Base change yes

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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-d
Dimension 8
Is CM no
Is base change yes
Parent newspace dimension 23

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 51x^{6} \) \(\mathstrut +\mathstrut 25x^{5} \) \(\mathstrut +\mathstrut 711x^{4} \) \(\mathstrut -\mathstrut 363x^{3} \) \(\mathstrut -\mathstrut 2619x^{2} \) \(\mathstrut +\mathstrut 432x \) \(\mathstrut +\mathstrut 1620\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $-1$
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 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $\phantom{-}e$
16 $[16, 2, 2]$ $\phantom{-}\frac{23}{6232}e^{7} - \frac{181}{28044}e^{6} - \frac{10225}{56088}e^{5} + \frac{22093}{56088}e^{4} + \frac{42041}{18696}e^{3} - \frac{26343}{6232}e^{2} - \frac{36387}{6232}e + \frac{12805}{3116}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}\frac{71}{14022}e^{7} + \frac{32}{7011}e^{6} - \frac{2905}{14022}e^{5} + \frac{421}{4674}e^{4} + \frac{3073}{1558}e^{3} - \frac{15049}{4674}e^{2} - \frac{1981}{1558}e + \frac{5935}{779}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $-\frac{13}{28044}e^{7} + \frac{49}{14022}e^{6} + \frac{883}{28044}e^{5} - \frac{5783}{28044}e^{4} - \frac{1989}{3116}e^{3} + \frac{27859}{9348}e^{2} + \frac{12717}{3116}e - \frac{9535}{1558}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{71}{14022}e^{7} + \frac{32}{7011}e^{6} - \frac{2905}{14022}e^{5} + \frac{421}{4674}e^{4} + \frac{3073}{1558}e^{3} - \frac{15049}{4674}e^{2} - \frac{1981}{1558}e + \frac{5935}{779}$
19 $[19, 19, w - 1]$ $-\frac{13}{28044}e^{7} + \frac{49}{14022}e^{6} + \frac{883}{28044}e^{5} - \frac{5783}{28044}e^{4} - \frac{1989}{3116}e^{3} + \frac{27859}{9348}e^{2} + \frac{12717}{3116}e - \frac{9535}{1558}$
29 $[29, 29, w^{2} - w - 8]$ $\phantom{-}\frac{65}{28044}e^{7} - \frac{245}{14022}e^{6} - \frac{4415}{28044}e^{5} + \frac{19567}{28044}e^{4} + \frac{6829}{3116}e^{3} - \frac{20465}{3116}e^{2} - \frac{10613}{3116}e + \frac{16515}{1558}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}\frac{65}{28044}e^{7} - \frac{245}{14022}e^{6} - \frac{4415}{28044}e^{5} + \frac{19567}{28044}e^{4} + \frac{6829}{3116}e^{3} - \frac{20465}{3116}e^{2} - \frac{10613}{3116}e + \frac{16515}{1558}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{16}{7011}e^{7} - \frac{179}{7011}e^{6} + \frac{128}{7011}e^{5} + \frac{634}{779}e^{4} + \frac{668}{779}e^{3} - \frac{14789}{2337}e^{2} - \frac{4842}{779}e + \frac{7090}{779}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $-\frac{16}{7011}e^{7} - \frac{179}{7011}e^{6} + \frac{128}{7011}e^{5} + \frac{634}{779}e^{4} + \frac{668}{779}e^{3} - \frac{14789}{2337}e^{2} - \frac{4842}{779}e + \frac{7090}{779}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $\phantom{-}\frac{1}{76}e^{7} + \frac{7}{342}e^{6} - \frac{395}{684}e^{5} - \frac{229}{684}e^{4} + \frac{1547}{228}e^{3} + \frac{17}{228}e^{2} - \frac{1321}{76}e - \frac{5}{38}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $\phantom{-}\frac{1}{76}e^{7} + \frac{7}{342}e^{6} - \frac{395}{684}e^{5} - \frac{229}{684}e^{4} + \frac{1547}{228}e^{3} + \frac{17}{228}e^{2} - \frac{1321}{76}e - \frac{5}{38}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $-\frac{49}{14022}e^{7} - \frac{55}{7011}e^{6} + \frac{2729}{14022}e^{5} + \frac{481}{1558}e^{4} - \frac{14701}{4674}e^{3} - \frac{14959}{4674}e^{2} + \frac{20129}{1558}e + \frac{5647}{779}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $-\frac{49}{14022}e^{7} - \frac{55}{7011}e^{6} + \frac{2729}{14022}e^{5} + \frac{481}{1558}e^{4} - \frac{14701}{4674}e^{3} - \frac{14959}{4674}e^{2} + \frac{20129}{1558}e + \frac{5647}{779}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{71}{14022}e^{7} + \frac{32}{7011}e^{6} - \frac{2905}{14022}e^{5} + \frac{421}{4674}e^{4} + \frac{10777}{4674}e^{3} - \frac{4497}{1558}e^{2} - \frac{12887}{1558}e + \frac{4377}{779}$
71 $[71, 71, w^{2} - 8]$ $\phantom{-}\frac{71}{14022}e^{7} + \frac{32}{7011}e^{6} - \frac{2905}{14022}e^{5} + \frac{421}{4674}e^{4} + \frac{10777}{4674}e^{3} - \frac{4497}{1558}e^{2} - \frac{12887}{1558}e + \frac{4377}{779}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $-\frac{421}{28044}e^{7} - \frac{91}{14022}e^{6} + \frac{19727}{28044}e^{5} - \frac{1465}{9348}e^{4} - \frac{77947}{9348}e^{3} + \frac{32839}{9348}e^{2} + \frac{61405}{3116}e - \frac{6775}{1558}$
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 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $1$