Properties

Base field 4.4.6125.1
Weight [2, 2, 2, 2]
Level norm 55
Level $[55,55,-2w^{3} - 3w^{2} + 13w + 14]$
Label 4.4.6125.1-55.2-b
Dimension 4
CM no
Base change no

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Base field 4.4.6125.1

Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 9x^{2} + 9x + 11\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[55,55,-2w^{3} - 3w^{2} + 13w + 14]$
Label 4.4.6125.1-55.2-b
Dimension 4
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{4} + 5x^{3} - 5x^{2} - 21x + 12\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
5 $[5, 5, -2w^{3} - 2w^{2} + 13w + 8]$ $\phantom{-}1$
11 $[11, 11, 2w^{3} + 3w^{2} - 12w - 11]$ $\phantom{-}e$
11 $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ $-\frac{1}{4}e^{3} - \frac{3}{2}e^{2} - \frac{1}{4}e + 3$
11 $[11, 11, w^{3} + w^{2} - 7w - 4]$ $\phantom{-}e$
11 $[11, 11, w - 1]$ $-1$
16 $[16, 2, 2]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{5}{2}e^{2} - e - 7$
19 $[19, 19, -w^{2} + 4]$ $-\frac{1}{2}e^{3} - \frac{5}{2}e^{2} + 4$
19 $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e - 2$
19 $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{3}{2}e - 2$
19 $[19, 19, -w^{3} - w^{2} + 5w + 3]$ $\phantom{-}\frac{1}{4}e^{3} + e^{2} - \frac{13}{4}e - 5$
49 $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ $-\frac{1}{4}e^{3} - e^{2} - \frac{3}{4}e - 5$
59 $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ $-\frac{1}{2}e^{3} - \frac{3}{2}e^{2} + 3e$
59 $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ $\phantom{-}e^{3} + \frac{9}{2}e^{2} - \frac{5}{2}e - 6$
59 $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ $-\frac{1}{4}e^{3} - e^{2} - \frac{7}{4}e - 3$
59 $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ $\phantom{-}\frac{3}{2}e^{2} + \frac{15}{2}e - 6$
71 $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ $-\frac{1}{4}e^{3} + \frac{17}{4}e - 3$
71 $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ $\phantom{-}e^{3} + \frac{13}{2}e^{2} + \frac{5}{2}e - 18$
71 $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ $-\frac{3}{2}e^{2} - \frac{9}{2}e + 6$
71 $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ $\phantom{-}\frac{1}{4}e^{3} - \frac{13}{4}e + 3$
81 $[81, 3, -3]$ $-\frac{3}{4}e^{3} - 2e^{2} + \frac{27}{4}e + 1$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
5 $[5,5,3w^{3} + 4w^{2} - 18w - 14]$ $-1$
11 $[11,11,-w + 1]$ $1$