Properties

Base field 4.4.725.1
Weight [2, 2, 2, 2]
Level norm 169
Level $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$
Label 4.4.725.1-169.1-a
Dimension 3
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.725.1

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

Form

Weight [2, 2, 2, 2]
Level $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$
Label 4.4.725.1-169.1-a
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 3

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut +\mathstrut 2x^{2} \) \(\mathstrut -\mathstrut 20x \) \(\mathstrut -\mathstrut 8\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
11 $[11, 11, -w^{3} + 2w^{2} + w - 3]$ $\phantom{-}e$
11 $[11, 11, w^{3} - 3w]$ $-\frac{1}{2}e + 1$
16 $[16, 2, 2]$ $-\frac{1}{4}e^{2} - \frac{3}{2}e + 3$
19 $[19, 19, -w^{3} + 2w + 2]$ $-\frac{1}{4}e^{2} + 5$
19 $[19, 19, 2w^{3} - 3w^{2} - 4w + 2]$ $-\frac{1}{8}e^{2} - \frac{1}{2}e + \frac{3}{2}$
25 $[25, 5, 2w^{3} - 2w^{2} - 4w + 1]$ $\phantom{-}\frac{3}{4}e^{2} + e - 9$
29 $[29, 29, w^{3} - w^{2} - 4w + 1]$ $\phantom{-}\frac{1}{4}e^{2} + e - 1$
31 $[31, 31, w^{3} - 4w + 1]$ $-\frac{1}{8}e^{2} + \frac{1}{2}e + \frac{3}{2}$
31 $[31, 31, -w^{2} + 2w + 3]$ $\phantom{-}\frac{1}{2}e^{2} - 6$
41 $[41, 41, 2w^{2} - w - 3]$ $-\frac{1}{4}e^{2} - e + 5$
41 $[41, 41, -w^{3} + 3w^{2} + w - 4]$ $-\frac{7}{8}e^{2} - \frac{1}{2}e + \frac{25}{2}$
49 $[49, 7, 2w^{3} - 3w^{2} - 5w + 2]$ $\phantom{-}\frac{1}{8}e^{2} + \frac{1}{2}e + \frac{1}{2}$
49 $[49, 7, w^{2} + w - 3]$ $\phantom{-}\frac{1}{8}e^{2} - \frac{3}{2}e - \frac{19}{2}$
61 $[61, 61, 2w^{3} - 3w^{2} - 4w]$ $\phantom{-}\frac{7}{8}e^{2} + \frac{7}{2}e - \frac{25}{2}$
61 $[61, 61, -3w^{3} + 4w^{2} + 7w - 3]$ $-\frac{1}{8}e^{2} + \frac{1}{2}e - \frac{5}{2}$
79 $[79, 79, 2w^{3} - 4w^{2} - 3w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 15$
79 $[79, 79, w^{3} + w^{2} - 3w - 5]$ $\phantom{-}\frac{1}{4}e^{2} + 2e + 3$
81 $[81, 3, -3]$ $\phantom{-}\frac{1}{4}e^{2} + \frac{3}{2}e - 6$
89 $[89, 89, -3w^{3} + 4w^{2} + 5w - 3]$ $-e^{2} + e + 18$
89 $[89, 89, 3w^{3} - 2w^{2} - 7w]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e - 4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
169 $[169, 13, -4w^{3} + 5w^{2} + 8w - 4]$ $1$