# Properties

 Base field 4.4.18688.1 Weight [2, 2, 2, 2] Level norm 34 Level $[34, 34, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w + \frac{8}{3}]$ Label 4.4.18688.1-34.1-j Dimension 14 CM no Base change no

# Related objects

• L-function not available

# Learn more about

## Base field 4.4.18688.1

Generator $w$, with minimal polynomial $x^{4} - 10x^{2} - 4x + 14$; narrow class number $2$ and class number $1$.

## Form

 Weight [2, 2, 2, 2] Level $[34, 34, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w + \frac{8}{3}]$ Label 4.4.18688.1-34.1-j Dimension 14 Is CM no Is base change no Parent newspace dimension 52

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$x^{14}$ $\mathstrut +\mathstrut 17x^{13}$ $\mathstrut +\mathstrut 80x^{12}$ $\mathstrut -\mathstrut 152x^{11}$ $\mathstrut -\mathstrut 2219x^{10}$ $\mathstrut -\mathstrut 3981x^{9}$ $\mathstrut +\mathstrut 10527x^{8}$ $\mathstrut +\mathstrut 31390x^{7}$ $\mathstrut -\mathstrut 22670x^{6}$ $\mathstrut -\mathstrut 85010x^{5}$ $\mathstrut +\mathstrut 51177x^{4}$ $\mathstrut +\mathstrut 87844x^{3}$ $\mathstrut -\mathstrut 82664x^{2}$ $\mathstrut +\mathstrut 11722x$ $\mathstrut +\mathstrut 3826$
Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $-1$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $...$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $...$
9 $[9, 3, w + 1]$ $...$
17 $[17, 17, w + 3]$ $...$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $\phantom{-}1$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $...$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $...$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $...$
41 $[41, 41, w^{2} - 5]$ $...$
41 $[41, 41, 2w + 3]$ $...$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $...$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $...$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $...$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $...$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $...$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $...$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $...$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $1$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $-1$