Properties

Base field 3.3.1129.1
Weight [2, 2, 2]
Level norm 11
Level $[11, 11, -w^{2} + 5]$
Label 3.3.1129.1-11.1-c
Dimension 6
CM no
Base change no

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Base field 3.3.1129.1

Generator \(w\), with minimal polynomial \(x^{3} - 7x - 3\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2]
Level $[11, 11, -w^{2} + 5]$
Label 3.3.1129.1-11.1-c
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:
\(x^{6} \) \(\mathstrut +\mathstrut 3x^{5} \) \(\mathstrut -\mathstrut 9x^{4} \) \(\mathstrut -\mathstrut 28x^{3} \) \(\mathstrut +\mathstrut 15x^{2} \) \(\mathstrut +\mathstrut 63x \) \(\mathstrut +\mathstrut 26\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}e$
3 $[3, 3, w + 1]$ $-\frac{1}{3}e^{4} - \frac{1}{3}e^{3} + \frac{7}{3}e^{2} + \frac{4}{3}e - \frac{1}{3}$
3 $[3, 3, w + 2]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 3e^{3} - \frac{14}{3}e^{2} + 6e + \frac{19}{3}$
8 $[8, 2, 2]$ $\phantom{-}\frac{1}{3}e^{4} + \frac{4}{3}e^{3} - \frac{1}{3}e^{2} - \frac{19}{3}e - \frac{23}{3}$
11 $[11, 11, -w^{2} + 5]$ $\phantom{-}1$
13 $[13, 13, w^{2} - w - 7]$ $\phantom{-}\frac{1}{3}e^{5} + e^{4} - \frac{5}{3}e^{3} - 6e^{2} + \frac{2}{3}e + \frac{20}{3}$
17 $[17, 17, -w^{2} + w + 4]$ $-\frac{2}{3}e^{4} - \frac{5}{3}e^{3} + \frac{11}{3}e^{2} + \frac{26}{3}e + \frac{1}{3}$
19 $[19, 19, -w^{2} - w + 4]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{4}{3}e^{4} - \frac{7}{3}e^{3} - \frac{28}{3}e^{2} + \frac{10}{3}e + 11$
29 $[29, 29, 2w^{2} - 2w - 11]$ $-\frac{1}{3}e^{5} - e^{4} + \frac{5}{3}e^{3} + 6e^{2} + \frac{1}{3}e - \frac{5}{3}$
31 $[31, 31, w^{2} - 2w - 4]$ $\phantom{-}e^{2} - 4$
37 $[37, 37, -2w^{2} + 3w + 7]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 4e^{3} - \frac{17}{3}e^{2} + 12e + \frac{34}{3}$
41 $[41, 41, w^{2} - 2]$ $\phantom{-}e^{4} + 2e^{3} - 5e^{2} - 8e$
59 $[59, 59, 2w^{2} - 13]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - 3e^{3} - \frac{17}{3}e^{2} + 6e + \frac{40}{3}$
61 $[61, 61, w^{2} + w - 10]$ $\phantom{-}e^{5} + \frac{5}{3}e^{4} - \frac{31}{3}e^{3} - \frac{41}{3}e^{2} + \frac{82}{3}e + \frac{86}{3}$
67 $[67, 67, 2w^{2} - w - 11]$ $-\frac{1}{3}e^{5} - e^{4} + \frac{2}{3}e^{3} + 4e^{2} + \frac{22}{3}e - \frac{2}{3}$
73 $[73, 73, -w^{2} - 1]$ $-e^{5} - \frac{7}{3}e^{4} + \frac{23}{3}e^{3} + \frac{37}{3}e^{2} - \frac{41}{3}e - \frac{19}{3}$
83 $[83, 83, w^{2} - w - 10]$ $-\frac{2}{3}e^{5} - 2e^{4} + \frac{16}{3}e^{3} + 12e^{2} - \frac{31}{3}e - \frac{25}{3}$
89 $[89, 89, -w^{2} + 4w - 2]$ $\phantom{-}e^{5} + \frac{1}{3}e^{4} - \frac{38}{3}e^{3} - \frac{13}{3}e^{2} + \frac{110}{3}e + \frac{52}{3}$
97 $[97, 97, w^{2} - 2w - 7]$ $-\frac{5}{3}e^{4} - \frac{11}{3}e^{3} + \frac{29}{3}e^{2} + \frac{50}{3}e + \frac{4}{3}$
97 $[97, 97, -w^{2} - 4w - 5]$ $-e^{5} - \frac{4}{3}e^{4} + \frac{35}{3}e^{3} + \frac{31}{3}e^{2} - \frac{110}{3}e - \frac{76}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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