Properties

Base field \(\Q(\zeta_{11})^+\)
Weight [2, 2, 2, 2, 2]
Level norm 131
Level $[131,131,-w^{4} + 2w^{3} + 3w^{2} - 3w - 1]$
Label 5.5.14641.1-131.4-b
Dimension 5
CM no
Base change no

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Base field \(\Q(\zeta_{11})^+\)

Generator \(w\), with minimal polynomial \(x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2, 2]
Level $[131,131,-w^{4} + 2w^{3} + 3w^{2} - 3w - 1]$
Label 5.5.14641.1-131.4-b
Dimension 5
Is CM no
Is base change no
Parent newspace dimension 6

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} \) \(\mathstrut -\mathstrut 6x^{4} \) \(\mathstrut -\mathstrut 13x^{3} \) \(\mathstrut +\mathstrut 146x^{2} \) \(\mathstrut -\mathstrut 295x \) \(\mathstrut +\mathstrut 164\)

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Norm Prime Eigenvalue
11 $[11, 11, w^{4} + w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}e$
23 $[23, 23, -w^{4} + 3w^{2} + 1]$ $\phantom{-}\frac{3}{2}e^{4} - \frac{19}{4}e^{3} - \frac{133}{4}e^{2} + \frac{499}{4}e - 81$
23 $[23, 23, -w^{4} + 3w^{2} + w - 2]$ $-e^{4} + 3e^{3} + 22e^{2} - 81e + 55$
23 $[23, 23, w^{4} - w^{3} - 3w^{2} + 3w + 2]$ $\phantom{-}\frac{3}{2}e^{4} - 5e^{3} - 33e^{2} + \frac{263}{2}e - 91$
23 $[23, 23, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $-e^{4} + 3e^{3} + 22e^{2} - 81e + 55$
23 $[23, 23, -w^{2} + w + 3]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{23}{2}e + 20$
32 $[32, 2, 2]$ $-\frac{1}{4}e^{4} + \frac{3}{4}e^{3} + \frac{25}{4}e^{2} - \frac{39}{2}e + 5$
43 $[43, 43, -2w^{4} + w^{3} + 6w^{2} - 2w - 1]$ $-e^{4} + \frac{7}{2}e^{3} + \frac{43}{2}e^{2} - \frac{185}{2}e + 71$
43 $[43, 43, -w^{4} + 2w^{2} + w + 1]$ $-\frac{1}{4}e^{4} + e^{3} + 6e^{2} - \frac{101}{4}e + 14$
43 $[43, 43, w^{3} + w^{2} - 4w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - \frac{1}{2}e^{2} - \frac{19}{2}e + 16$
43 $[43, 43, 2w^{4} - w^{3} - 7w^{2} + 3w + 3]$ $-e^{4} + 3e^{3} + 22e^{2} - 79e + 51$
43 $[43, 43, w^{4} - w^{3} - 4w^{2} + 4w + 2]$ $-e^{4} + 3e^{3} + 22e^{2} - 79e + 51$
67 $[67, 67, 2w^{4} - 7w^{2} + 2]$ $-\frac{5}{4}e^{4} + 4e^{3} + 28e^{2} - \frac{425}{4}e + 69$
67 $[67, 67, w^{4} - 2w^{3} - 3w^{2} + 6w + 2]$ $-e^{4} + 4e^{3} + 21e^{2} - 104e + 91$
67 $[67, 67, 2w^{4} - 7w^{2} - w + 4]$ $\phantom{-}\frac{7}{2}e^{4} - \frac{23}{2}e^{3} - \frac{151}{2}e^{2} + 303e - 225$
67 $[67, 67, w^{4} - 2w^{3} - 4w^{2} + 6w + 2]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{7}{4}e^{3} - \frac{45}{4}e^{2} + \frac{183}{4}e - 30$
67 $[67, 67, -w^{4} + w^{3} + 5w^{2} - 3w - 3]$ $\phantom{-}\frac{1}{2}e^{4} - 2e^{3} - 11e^{2} + \frac{105}{2}e - 40$
89 $[89, 89, w^{3} + w^{2} - 4w - 1]$ $-\frac{1}{2}e^{4} + \frac{5}{4}e^{3} + \frac{43}{4}e^{2} - \frac{141}{4}e + 23$
89 $[89, 89, -2w^{4} + w^{3} + 7w^{2} - 3w - 2]$ $\phantom{-}\frac{1}{2}e^{4} - \frac{3}{2}e^{3} - \frac{23}{2}e^{2} + 41e - 22$
89 $[89, 89, -w^{4} + w^{3} + 4w^{2} - 4w - 3]$ $-3e^{4} + \frac{19}{2}e^{3} + \frac{131}{2}e^{2} - \frac{509}{2}e + 179$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
131 $[131,131,-w^{4} + 2w^{3} + 3w^{2} - 3w - 1]$ $-1$