# Properties

 Base field 4.4.8768.1 Weight [2, 2, 2, 2] Level norm 28 Level $[28,14,w^{3} - 4w - 1]$ Label 4.4.8768.1-28.3-d Dimension 4 CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.8768.1

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 5x^{2} + 6x + 7$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[28,14,w^{3} - 4w - 1]$ Label 4.4.8768.1-28.3-d Dimension 4 Is CM no Is base change no Parent newspace dimension 14

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{4}$$ $$\mathstrut -\mathstrut 4x^{3}$$ $$\mathstrut -\mathstrut 13x^{2}$$ $$\mathstrut +\mathstrut 34x$$ $$\mathstrut +\mathstrut 71$$
Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $-1$
7 $[7, 7, w]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + \frac{13}{2}$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}e^{3} - \frac{5}{2}e^{2} - \frac{15}{2}e + \frac{7}{2}$
7 $[7, 7, w^{2} - 2]$ $-1$
7 $[7, 7, w - 1]$ $\phantom{-}e$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}\frac{1}{2}e^{3} + \frac{3}{2}e^{2} - \frac{19}{2}e - 21$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $-\frac{1}{2}e^{3} - e^{2} + 9e + \frac{35}{2}$
31 $[31, 31, w^{2} - 5]$ $-e^{3} + \frac{3}{2}e^{2} + \frac{17}{2}e + \frac{15}{2}$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}\frac{9}{2}e^{2} - \frac{19}{2}e - \frac{75}{2}$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $\phantom{-}e^{3} - 3e^{2} - 6e + 14$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $-e^{2} + e + 9$
47 $[47, 47, w^{2} - 2w - 5]$ $-\frac{1}{2}e^{3} + 2e^{2} + 3e - \frac{3}{2}$
47 $[47, 47, w^{2} - 6]$ $-\frac{1}{2}e^{3} + \frac{13}{2}e^{2} - \frac{17}{2}e - 45$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}e^{3} - 7e^{2} + 3e + 44$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-2e^{3} + 3e^{2} + 19e + 11$
79 $[79, 79, -w - 3]$ $\phantom{-}e^{3} - 7e^{2} + 2e + 39$
79 $[79, 79, w - 4]$ $-\frac{1}{2}e^{3} + \frac{23}{2}e^{2} - \frac{35}{2}e - 89$
81 $[81, 3, -3]$ $-\frac{1}{2}e^{3} + e^{2} + 3e - \frac{9}{2}$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}3e^{3} - 12e^{2} - 13e + 52$
89 $[89, 89, w^{2} + w - 4]$ $-\frac{1}{2}e^{3} + e^{2} + 4e + \frac{15}{2}$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
4 $[4,2,-w^{2} + w + 3]$ $1$
7 $[7,7,-w^{2} + 2]$ $1$