# Properties

 Label 4.4.5725.1-79.1-e Base field 4.4.5725.1 Weight $[2, 2, 2, 2]$ Level norm $79$ Level $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ Dimension $6$ CM no Base change no

# Related objects

• L-function not available

## Base field 4.4.5725.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 8x^{2} + 6x + 11$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ Dimension: $6$ CM: no Base change: no Newspace dimension: $27$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{6} + 5x^{5} - 11x^{4} - 111x^{3} - 248x^{2} - 225x - 72$$
Norm Prime Eigenvalue
9 $[9, 3, \frac{1}{3}w^{3} - \frac{8}{3}w - \frac{2}{3}]$ $\phantom{-}e$
9 $[9, 3, -w + 1]$ $\phantom{-}e^{5} + 3e^{4} - 17e^{3} - 77e^{2} - 94e - 38$
11 $[11, 11, w]$ $\phantom{-}\frac{5}{3}e^{5} + \frac{19}{3}e^{4} - \frac{79}{3}e^{3} - 154e^{2} - \frac{661}{3}e - 92$
11 $[11, 11, -\frac{1}{3}w^{3} + \frac{2}{3}w + \frac{5}{3}]$ $-\frac{5}{3}e^{5} - \frac{16}{3}e^{4} + \frac{85}{3}e^{3} + 135e^{2} + \frac{487}{3}e + 53$
11 $[11, 11, \frac{1}{3}w^{3} - \frac{8}{3}w + \frac{1}{3}]$ $-\frac{11}{3}e^{5} - \frac{40}{3}e^{4} + \frac{175}{3}e^{3} + 327e^{2} + \frac{1402}{3}e + 201$
11 $[11, 11, -\frac{2}{3}w^{3} + \frac{13}{3}w + \frac{4}{3}]$ $\phantom{-}\frac{10}{3}e^{5} + \frac{35}{3}e^{4} - \frac{161}{3}e^{3} - 289e^{2} - \frac{1208}{3}e - 168$
16 $[16, 2, 2]$ $\phantom{-}e^{5} + 3e^{4} - 17e^{3} - 77e^{2} - 93e - 36$
25 $[25, 5, \frac{2}{3}w^{3} - \frac{10}{3}w - \frac{1}{3}]$ $\phantom{-}\frac{1}{3}e^{5} + \frac{2}{3}e^{4} - \frac{20}{3}e^{3} - 20e^{2} - \frac{14}{3}e + 9$
29 $[29, 29, -w - 3]$ $-4e^{5} - 15e^{4} + 63e^{3} + 365e^{2} + 531e + 232$
29 $[29, 29, -\frac{1}{3}w^{3} + \frac{8}{3}w - \frac{10}{3}]$ $-\frac{17}{3}e^{5} - \frac{58}{3}e^{4} + \frac{277}{3}e^{3} + 482e^{2} + \frac{1957}{3}e + 261$
31 $[31, 31, w^{3} - 6w + 1]$ $\phantom{-}e^{5} + 4e^{4} - 15e^{3} - 96e^{2} - 153e - 74$
31 $[31, 31, w^{3} - 6w - 2]$ $\phantom{-}\frac{11}{3}e^{5} + \frac{43}{3}e^{4} - \frac{172}{3}e^{3} - 345e^{2} - \frac{1528}{3}e - 228$
41 $[41, 41, \frac{2}{3}w^{3} + w^{2} - \frac{13}{3}w - \frac{10}{3}]$ $\phantom{-}\frac{8}{3}e^{5} + \frac{31}{3}e^{4} - \frac{124}{3}e^{3} - 250e^{2} - \frac{1123}{3}e - 163$
41 $[41, 41, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{5}{3}]$ $\phantom{-}e^{5} + 3e^{4} - 17e^{3} - 78e^{2} - 94e - 25$
59 $[59, 59, \frac{2}{3}w^{3} - \frac{13}{3}w + \frac{8}{3}]$ $-5e^{5} - 19e^{4} + 77e^{3} + 462e^{2} + 698e + 317$
59 $[59, 59, w^{3} + w^{2} - 6w - 4]$ $\phantom{-}2e^{5} + 8e^{4} - 30e^{3} - 192e^{2} - 306e - 146$
79 $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $\phantom{-}1$
79 $[79, 79, \frac{1}{3}w^{3} + w^{2} - \frac{2}{3}w - \frac{17}{3}]$ $\phantom{-}\frac{20}{3}e^{5} + \frac{73}{3}e^{4} - \frac{325}{3}e^{3} - 596e^{2} - \frac{2428}{3}e - 311$
89 $[89, 89, \frac{4}{3}w^{3} - \frac{23}{3}w - \frac{5}{3}]$ $\phantom{-}4e^{5} + 15e^{4} - 65e^{3} - 364e^{2} - 496e - 194$
89 $[89, 89, \frac{1}{3}w^{3} + 2w^{2} - \frac{5}{3}w - \frac{32}{3}]$ $-8e^{5} - 28e^{4} + 130e^{3} + 692e^{2} + 946e + 392$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$79$ $[79, 79, \frac{2}{3}w^{3} + w^{2} - \frac{10}{3}w - \frac{19}{3}]$ $-1$