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: | $[55,55,w^{3} + 2w^{2} - 5w - 6]$ |
Dimension: | $5$ |
CM: | no |
Base change: | no |
Newspace dimension: | $18$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{5} + 3x^{4} - 39x^{3} - 119x^{2} + 322x + 920\) |
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 | $[11, 11, -w^{3} - 2w^{2} + 6w + 9]$ | $\phantom{-}1$ |
11 | $[11, 11, w^{3} + w^{2} - 7w - 4]$ | $\phantom{-}\frac{5}{16}e^{4} - \frac{1}{2}e^{3} - \frac{155}{16}e^{2} + \frac{67}{8}e + \frac{117}{2}$ |
11 | $[11, 11, w - 1]$ | $-\frac{3}{8}e^{4} + \frac{1}{2}e^{3} + \frac{97}{8}e^{2} - \frac{33}{4}e - 79$ |
16 | $[16, 2, 2]$ | $\phantom{-}\frac{7}{16}e^{4} - \frac{3}{4}e^{3} - \frac{221}{16}e^{2} + \frac{101}{8}e + \frac{169}{2}$ |
19 | $[19, 19, -w^{2} + 4]$ | $-\frac{1}{8}e^{4} + \frac{1}{4}e^{3} + \frac{33}{8}e^{2} - \frac{17}{4}e - 27$ |
19 | $[19, 19, 2w^{3} + 2w^{2} - 13w - 6]$ | $-\frac{3}{16}e^{4} + \frac{1}{4}e^{3} + \frac{105}{16}e^{2} - \frac{33}{8}e - \frac{91}{2}$ |
19 | $[19, 19, 3w^{3} + 4w^{2} - 18w - 16]$ | $\phantom{-}\frac{7}{16}e^{4} - \frac{3}{4}e^{3} - \frac{221}{16}e^{2} + \frac{101}{8}e + \frac{175}{2}$ |
19 | $[19, 19, -w^{3} - w^{2} + 5w + 3]$ | $\phantom{-}\frac{1}{16}e^{4} - \frac{1}{4}e^{3} - \frac{27}{16}e^{2} + \frac{43}{8}e + \frac{21}{2}$ |
49 | $[49, 7, 2w^{3} + 3w^{2} - 13w - 15]$ | $\phantom{-}\frac{3}{4}e^{4} - \frac{5}{4}e^{3} - \frac{49}{2}e^{2} + 22e + 166$ |
59 | $[59, 59, -3w^{3} - 4w^{2} + 19w + 14]$ | $\phantom{-}\frac{7}{16}e^{4} - \frac{3}{4}e^{3} - \frac{221}{16}e^{2} + \frac{109}{8}e + \frac{179}{2}$ |
59 | $[59, 59, 3w^{3} + 4w^{2} - 18w - 17]$ | $-\frac{11}{16}e^{4} + \frac{5}{4}e^{3} + \frac{353}{16}e^{2} - \frac{177}{8}e - \frac{283}{2}$ |
59 | $[59, 59, 2w^{3} + 3w^{2} - 11w - 13]$ | $-\frac{9}{16}e^{4} + \frac{3}{4}e^{3} + \frac{283}{16}e^{2} - \frac{99}{8}e - \frac{217}{2}$ |
59 | $[59, 59, -w^{3} - 2w^{2} + 7w + 9]$ | $\phantom{-}e^{4} - \frac{5}{4}e^{3} - \frac{129}{4}e^{2} + \frac{41}{2}e + 208$ |
71 | $[71, 71, 3w^{3} + 3w^{2} - 17w - 10]$ | $-\frac{7}{16}e^{4} + \frac{3}{4}e^{3} + \frac{237}{16}e^{2} - \frac{109}{8}e - \frac{203}{2}$ |
71 | $[71, 71, -2w^{3} - w^{2} + 14w + 2]$ | $-\frac{5}{16}e^{4} + \frac{3}{4}e^{3} + \frac{159}{16}e^{2} - \frac{111}{8}e - \frac{129}{2}$ |
71 | $[71, 71, 5w^{3} + 7w^{2} - 30w - 25]$ | $\phantom{-}\frac{1}{4}e^{3} + \frac{1}{4}e^{2} - \frac{13}{2}e - 6$ |
71 | $[71, 71, -3w^{3} - 4w^{2} + 16w + 16]$ | $\phantom{-}\frac{1}{8}e^{4} - \frac{1}{4}e^{3} - \frac{41}{8}e^{2} + \frac{21}{4}e + 43$ |
81 | $[81, 3, -3]$ | $-\frac{1}{4}e^{4} + \frac{1}{4}e^{3} + 8e^{2} - 5e - 54$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$5$ | $[5,5,-w^{3} - w^{2} + 5w + 5]$ | $-1$ |
$11$ | $[11,11,-w^{3} - 2w^{2} + 6w + 9]$ | $-1$ |