# Properties

 Base field $$\Q(\sqrt{5}, \sqrt{7})$$ Weight [2, 2, 2, 2] Level norm 19 Level $[19,19,\frac{2}{23}w^{3} - \frac{3}{23}w^{2} + \frac{3}{23}w + \frac{22}{23}]$ Label 4.4.19600.1-19.4-b Dimension 20 CM no Base change no

# Related objects

• L-function not available

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## Base field $$\Q(\sqrt{5}, \sqrt{7})$$

Generator $$w$$, with minimal polynomial $$x^{4} - 2x^{3} - 15x^{2} + 16x + 29$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight [2, 2, 2, 2] Level $[19,19,\frac{2}{23}w^{3} - \frac{3}{23}w^{2} + \frac{3}{23}w + \frac{22}{23}]$ Label 4.4.19600.1-19.4-b Dimension 20 Is CM no Is base change no Parent newspace dimension 40

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{20}$$ $$\mathstrut +\mathstrut 4x^{19}$$ $$\mathstrut -\mathstrut 33x^{18}$$ $$\mathstrut -\mathstrut 130x^{17}$$ $$\mathstrut +\mathstrut 447x^{16}$$ $$\mathstrut +\mathstrut 1669x^{15}$$ $$\mathstrut -\mathstrut 3326x^{14}$$ $$\mathstrut -\mathstrut 10888x^{13}$$ $$\mathstrut +\mathstrut 15487x^{12}$$ $$\mathstrut +\mathstrut 38604x^{11}$$ $$\mathstrut -\mathstrut 47385x^{10}$$ $$\mathstrut -\mathstrut 71872x^{9}$$ $$\mathstrut +\mathstrut 91709x^{8}$$ $$\mathstrut +\mathstrut 56127x^{7}$$ $$\mathstrut -\mathstrut 97476x^{6}$$ $$\mathstrut +\mathstrut 5121x^{5}$$ $$\mathstrut +\mathstrut 39385x^{4}$$ $$\mathstrut -\mathstrut 20842x^{3}$$ $$\mathstrut +\mathstrut 3795x^{2}$$ $$\mathstrut -\mathstrut 92x$$ $$\mathstrut -\mathstrut 28$$
Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $\phantom{-}e$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $...$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $...$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $...$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $...$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $...$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $\phantom{-}1$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $...$
29 $[29, 29, w]$ $...$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $...$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $...$
29 $[29, 29, -w + 1]$ $...$
31 $[31, 31, w + 2]$ $...$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $...$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $...$
31 $[31, 31, -w + 3]$ $...$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $...$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $...$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $...$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,\frac{2}{23}w^{3} - \frac{3}{23}w^{2} + \frac{3}{23}w + \frac{22}{23}]$ $-1$