Properties

Base field 5.5.160801.1
Weight [2, 2, 2, 2, 2]
Level norm 3
Level $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$
Label 5.5.160801.1-3.1-b
Dimension 4
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 5.5.160801.1

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

Form

Weight [2, 2, 2, 2, 2]
Level $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$
Label 5.5.160801.1-3.1-b
Dimension 4
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:
\(x^{4} \) \(\mathstrut -\mathstrut 3x^{3} \) \(\mathstrut -\mathstrut 22x^{2} \) \(\mathstrut +\mathstrut 61x \) \(\mathstrut +\mathstrut 43\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w^{4} - w^{3} - 5w^{2} + 3w + 3]$ $\phantom{-}1$
9 $[9, 3, -w^{4} + 5w^{2} - 3]$ $\phantom{-}e$
9 $[9, 3, -w^{4} + w^{3} + 5w^{2} - 3w - 2]$ $-e + 1$
13 $[13, 13, -w^{4} + w^{3} + 4w^{2} - 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + e^{2} - 9e - \frac{23}{2}$
17 $[17, 17, w^{4} - w^{3} - 5w^{2} + 3w + 1]$ $\phantom{-}e^{3} + e^{2} - 18e - 9$
19 $[19, 19, -w^{3} + w^{2} + 4w - 2]$ $\phantom{-}\frac{1}{2}e^{3} - 9e - \frac{1}{2}$
23 $[23, 23, -w^{2} + 3]$ $\phantom{-}\frac{1}{2}e^{3} - 9e + \frac{7}{2}$
31 $[31, 31, w^{3} - 4w + 2]$ $-e^{3} - e^{2} + 17e + 12$
32 $[32, 2, 2]$ $-\frac{1}{2}e^{3} - e^{2} + 10e + \frac{21}{2}$
37 $[37, 37, w^{3} - 3w - 1]$ $\phantom{-}e^{3} + e^{2} - 18e - 8$
53 $[53, 53, -2w^{4} + w^{3} + 9w^{2} - 3w - 2]$ $-2e^{3} - 2e^{2} + 35e + 23$
59 $[59, 59, -w^{4} + 5w^{2} + w - 4]$ $-2e + 4$
61 $[61, 61, -w^{4} + w^{3} + 5w^{2} - 4w]$ $-e^{3} + 19e - 2$
67 $[67, 67, -w^{4} + 6w^{2} + 2w - 4]$ $-e^{3} + 18e - 5$
71 $[71, 71, 2w^{4} - w^{3} - 9w^{2} + 4w + 5]$ $-e^{3} + 18e - 1$
79 $[79, 79, 2w^{4} - w^{3} - 10w^{2} + 2w + 7]$ $\phantom{-}4$
83 $[83, 83, -w^{4} + 2w^{3} + 5w^{2} - 7w - 2]$ $-2e^{3} - 3e^{2} + 35e + 39$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 3w + 3]$ $-\frac{1}{2}e^{3} + 9e - \frac{19}{2}$
83 $[83, 83, w^{4} - w^{3} - 5w^{2} + 4w - 1]$ $\phantom{-}\frac{1}{2}e^{3} - 7e + \frac{11}{2}$
83 $[83, 83, -w^{4} + w^{3} + 4w^{2} - 4w - 2]$ $-2e^{3} - 2e^{2} + 36e + 24$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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