Properties

Base field 4.4.11525.1
Weight [2, 2, 2, 2]
Level norm 11
Level $[11,11,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$
Label 4.4.11525.1-11.2-e
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 $[11,11,\frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$
Label 4.4.11525.1-11.2-e
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 8

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} \) \(\mathstrut -\mathstrut 20x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut +\mathstrut 52\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, \frac{1}{5}w^{3} + \frac{4}{5}w^{2} - \frac{11}{5}w - 7]$ $\phantom{-}e$
5 $[5, 5, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{1}{5}w + 4]$ $-\frac{3}{34}e^{3} - \frac{2}{17}e^{2} + \frac{16}{17}e + \frac{50}{17}$
11 $[11, 11, w + 1]$ $\phantom{-}\frac{3}{17}e^{3} - \frac{9}{34}e^{2} - \frac{32}{17}e + \frac{70}{17}$
11 $[11, 11, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w + 2]$ $-1$
16 $[16, 2, 2]$ $-\frac{3}{34}e^{3} + \frac{13}{34}e^{2} + \frac{16}{17}e - \frac{86}{17}$
19 $[19, 19, -\frac{1}{5}w^{3} + \frac{1}{5}w^{2} + \frac{1}{5}w + 1]$ $\phantom{-}\frac{1}{34}e^{3} - \frac{5}{17}e^{2} + \frac{6}{17}e + \frac{40}{17}$
19 $[19, 19, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{11}{5}w]$ $\phantom{-}\frac{9}{34}e^{3} - \frac{5}{34}e^{2} - \frac{82}{17}e + \frac{20}{17}$
19 $[19, 19, -\frac{2}{5}w^{3} + \frac{2}{5}w^{2} + \frac{17}{5}w]$ $\phantom{-}\frac{1}{34}e^{3} - \frac{5}{17}e^{2} + \frac{6}{17}e + \frac{40}{17}$
19 $[19, 19, w - 1]$ $-\frac{1}{17}e^{3} - \frac{7}{17}e^{2} + \frac{5}{17}e + \frac{90}{17}$
29 $[29, 29, w^{2} - w - 8]$ $-\frac{3}{34}e^{3} - \frac{2}{17}e^{2} + \frac{50}{17}e + \frac{84}{17}$
29 $[29, 29, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{7}{5}w + 2]$ $\phantom{-}\frac{5}{34}e^{3} + \frac{1}{34}e^{2} - \frac{38}{17}e + \frac{64}{17}$
31 $[31, 31, \frac{1}{5}w^{3} - \frac{1}{5}w^{2} - \frac{1}{5}w + 2]$ $-\frac{2}{17}e^{3} + \frac{3}{17}e^{2} + \frac{10}{17}e + \frac{44}{17}$
31 $[31, 31, \frac{2}{5}w^{3} - \frac{2}{5}w^{2} - \frac{17}{5}w + 3]$ $-\frac{4}{17}e^{3} + \frac{6}{17}e^{2} + \frac{37}{17}e - \frac{48}{17}$
61 $[61, 61, -\frac{2}{5}w^{3} - \frac{3}{5}w^{2} + \frac{12}{5}w + 5]$ $-\frac{2}{17}e^{3} + \frac{3}{17}e^{2} + \frac{61}{17}e + \frac{78}{17}$
61 $[61, 61, -\frac{4}{5}w^{3} - \frac{6}{5}w^{2} + \frac{39}{5}w + 15]$ $-\frac{2}{17}e^{3} + \frac{3}{17}e^{2} + \frac{10}{17}e - \frac{109}{17}$
61 $[61, 61, \frac{3}{5}w^{3} + \frac{2}{5}w^{2} - \frac{18}{5}w - 3]$ $\phantom{-}\frac{9}{17}e^{3} - \frac{5}{17}e^{2} - \frac{164}{17}e - \frac{11}{17}$
61 $[61, 61, \frac{7}{5}w^{3} + \frac{3}{5}w^{2} - \frac{62}{5}w - 13]$ $\phantom{-}\frac{1}{17}e^{3} + \frac{31}{34}e^{2} - \frac{22}{17}e - \frac{124}{17}$
71 $[71, 71, \frac{1}{5}w^{3} - \frac{6}{5}w^{2} - \frac{6}{5}w + 4]$ $\phantom{-}\frac{3}{34}e^{3} + \frac{2}{17}e^{2} - \frac{16}{17}e + \frac{86}{17}$
71 $[71, 71, w^{2} - 8]$ $-\frac{3}{34}e^{3} + \frac{13}{34}e^{2} + \frac{16}{17}e - \frac{188}{17}$
79 $[79, 79, \frac{3}{5}w^{3} + \frac{12}{5}w^{2} - \frac{33}{5}w - 22]$ $\phantom{-}\frac{1}{17}e^{3} + \frac{7}{17}e^{2} - \frac{22}{17}e - \frac{73}{17}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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