# Properties

 Label 4.4.13888.1-23.1-d Base field 4.4.13888.1 Weight $[2, 2, 2, 2]$ Level norm $23$ Level $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ Dimension $4$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.13888.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 7x^{2} + 6x + 9$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $28$

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{4} - 6x^{3} - 3x^{2} + 36x - 27$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{4}{3}w - 1]$ $\phantom{-}\frac{2}{9}e^{3} - e^{2} - \frac{8}{3}e + 4$
7 $[7, 7, \frac{1}{3}w^{3} - \frac{2}{3}w^{2} - \frac{7}{3}w + 1]$ $-\frac{2}{9}e^{3} + e^{2} + \frac{5}{3}e - 4$
7 $[7, 7, w - 2]$ $-\frac{1}{3}e^{3} + \frac{4}{3}e^{2} + 3e - 5$
7 $[7, 7, w - 1]$ $\phantom{-}\frac{2}{9}e^{3} - e^{2} - \frac{5}{3}e + 4$
9 $[9, 3, w]$ $\phantom{-}\frac{1}{3}e^{2} - e - 2$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{7}{3}w - 2]$ $\phantom{-}\frac{1}{9}e^{3} - \frac{2}{3}e^{2} - \frac{1}{3}e + 3$
23 $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $\phantom{-}1$
23 $[23, 23, -\frac{2}{3}w^{3} + \frac{4}{3}w^{2} + \frac{11}{3}w - 4]$ $-\frac{2}{9}e^{3} + e^{2} + \frac{8}{3}e - 1$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{1}{3}w^{2} + \frac{14}{3}w + 2]$ $-5$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 7]$ $\phantom{-}\frac{4}{9}e^{3} - 2e^{2} - \frac{10}{3}e + 8$
41 $[41, 41, -\frac{1}{3}w^{3} + \frac{5}{3}w^{2} + \frac{4}{3}w - 4]$ $-\frac{1}{3}e^{3} + 2e^{2} + e - 9$
47 $[47, 47, \frac{1}{3}w^{3} - \frac{5}{3}w^{2} - \frac{1}{3}w + 5]$ $\phantom{-}\frac{4}{3}e^{3} - 6e^{2} - 10e + 24$
47 $[47, 47, w^{2} - w - 4]$ $\phantom{-}\frac{7}{9}e^{3} - 3e^{2} - \frac{22}{3}e + 11$
73 $[73, 73, -w^{3} + 3w^{2} + 4w - 8]$ $\phantom{-}\frac{2}{9}e^{3} - 2e^{2} + \frac{4}{3}e + 10$
73 $[73, 73, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} - \frac{1}{3}w - 4]$ $-\frac{10}{9}e^{3} + 5e^{2} + \frac{40}{3}e - 26$
73 $[73, 73, -w^{3} + w^{2} + 7w + 1]$ $\phantom{-}\frac{4}{9}e^{3} - 2e^{2} - \frac{16}{3}e + 8$
73 $[73, 73, \frac{2}{3}w^{3} - \frac{4}{3}w^{2} - \frac{14}{3}w + 5]$ $\phantom{-}\frac{2}{9}e^{3} - \frac{14}{3}e - 2$
79 $[79, 79, w^{2} - 5]$ $\phantom{-}e^{3} - \frac{16}{3}e^{2} - 5e + 23$
79 $[79, 79, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{8}{3}w - 6]$ $-\frac{1}{3}e^{3} + \frac{2}{3}e^{2} + 5e - 1$
97 $[97, 97, -\frac{2}{3}w^{3} + \frac{7}{3}w^{2} + \frac{5}{3}w - 4]$ $\phantom{-}e^{3} - \frac{14}{3}e^{2} - 7e + 19$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$23$ $[23, 23, -\frac{1}{3}w^{3} + \frac{2}{3}w^{2} + \frac{1}{3}w - 2]$ $-1$