# Properties

 Base field $$\Q(\sqrt{2}, \sqrt{3})$$ Weight [2, 2, 2, 2] Level norm 719 Level $[719, 719, 3w^{3} - w^{2} - 13w - 2]$ Label 4.4.2304.1-719.1-d Dimension 42 CM no Base change no

# Related objects

• L-function not available

## Base field $$\Q(\sqrt{2}, \sqrt{3})$$

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

## Form

 Weight [2, 2, 2, 2] Level $[719, 719, 3w^{3} - w^{2} - 13w - 2]$ Label 4.4.2304.1-719.1-d Dimension 42 Is CM no Is base change no Parent newspace dimension 86

## Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
$$x^{42} + 14x^{41} + 34x^{40} - 408x^{39} - 2350x^{38} + 2872x^{37} + 47959x^{36} + 45628x^{35} - 513661x^{34} - 1177858x^{33} + 3138296x^{32} + 12471588x^{31} - 8881622x^{30} - 81149154x^{29} - 19451288x^{28} + 355762746x^{27} + 319264060x^{26} - 1072049282x^{25} - 1629606937x^{24} + 2144318806x^{23} + 5129126439x^{22} - 2381674306x^{21} - 11085644160x^{20} - 308615876x^{19} + 16896839028x^{18} + 6350069250x^{17} - 18014670387x^{16} - 12204571440x^{15} + 12842696420x^{14} + 13203331242x^{13} - 5334602069x^{12} - 9080703890x^{11} + 519961834x^{10} + 3950218108x^{9} + 673041312x^{8} - 999987480x^{7} - 355981022x^{6} + 113244286x^{5} + 69424342x^{4} + 1097070x^{3} - 4167805x^{2} - 628128x - 16200$$
Norm Prime Eigenvalue
2 $[2, 2, w^{3} - 4w + 1]$ $\phantom{-}e$
9 $[9, 3, -w^{2} + 2]$ $...$
23 $[23, 23, w^{3} - w^{2} - 4w + 1]$ $...$
23 $[23, 23, w^{2} - w - 3]$ $...$
23 $[23, 23, -w^{2} - w + 3]$ $...$
23 $[23, 23, -w^{3} - w^{2} + 4w + 1]$ $...$
25 $[25, 5, w^{3} - 5w + 1]$ $...$
25 $[25, 5, w^{3} - 5w - 1]$ $...$
47 $[47, 47, -3w^{3} + 2w^{2} + 12w - 8]$ $...$
47 $[47, 47, -2w^{3} - w^{2} + 6w]$ $...$
47 $[47, 47, 2w^{3} - w^{2} - 6w]$ $...$
47 $[47, 47, w^{2} + w - 5]$ $...$
49 $[49, 7, 2w^{3} - 6w - 1]$ $...$
49 $[49, 7, -2w^{3} + 6w - 1]$ $...$
71 $[71, 71, 2w^{3} - w^{2} - 7w + 1]$ $...$
71 $[71, 71, 3w^{3} - w^{2} - 11w + 2]$ $...$
71 $[71, 71, 4w^{3} - 2w^{2} - 14w + 5]$ $...$
71 $[71, 71, -3w^{3} + 2w^{2} + 10w - 4]$ $...$
73 $[73, 73, -w^{3} - 2w^{2} + 3w + 5]$ $...$
73 $[73, 73, -w^{3} + 2w^{2} + 3w - 3]$ $...$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
719 $[719,719,3w^{3}-w^{2}-13w-2]$ $-1$