Properties

Label 4.4.19429.1-15.1-d
Base field 4.4.19429.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, w^{2} - 2w - 5]$
Dimension $6$
CM no
Base change no

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Base field 4.4.19429.1

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

Form

Weight: $[2, 2, 2, 2]$
Level: $[15, 15, w^{2} - 2w - 5]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $25$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} - 3x^{5} - 12x^{4} + 15x^{3} + 38x^{2} + 14x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $\phantom{-}1$
5 $[5, 5, w]$ $-1$
7 $[7, 7, -w^{3} + 2w^{2} + 4w - 3]$ $\phantom{-}e$
13 $[13, 13, -w^{2} + w + 4]$ $-e^{5} + 3e^{4} + 12e^{3} - 16e^{2} - 36e - 9$
13 $[13, 13, -w^{3} + 2w^{2} + 5w - 2]$ $\phantom{-}e^{2} - 2e - 5$
16 $[16, 2, 2]$ $\phantom{-}\frac{4}{3}e^{5} - \frac{14}{3}e^{4} - \frac{41}{3}e^{3} + \frac{79}{3}e^{2} + 38e + \frac{11}{3}$
17 $[17, 17, -w + 2]$ $-\frac{5}{3}e^{5} + \frac{16}{3}e^{4} + \frac{58}{3}e^{3} - \frac{89}{3}e^{2} - 61e - \frac{34}{3}$
19 $[19, 19, -w^{3} + 2w^{2} + 3w - 2]$ $\phantom{-}\frac{7}{3}e^{5} - \frac{23}{3}e^{4} - \frac{77}{3}e^{3} + \frac{124}{3}e^{2} + 76e + \frac{41}{3}$
27 $[27, 3, w^{3} - 3w^{2} - 4w + 7]$ $-2e^{5} + 7e^{4} + 20e^{3} - 39e^{2} - 52e - 4$
31 $[31, 31, w^{3} - 3w^{2} - 3w + 7]$ $\phantom{-}e^{5} - 3e^{4} - 13e^{3} + 18e^{2} + 44e + 6$
31 $[31, 31, -w^{3} + w^{2} + 6w + 1]$ $-\frac{4}{3}e^{5} + \frac{14}{3}e^{4} + \frac{41}{3}e^{3} - \frac{79}{3}e^{2} - 40e - \frac{17}{3}$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}2e^{5} - 6e^{4} - 24e^{3} + 31e^{2} + 73e + 19$
43 $[43, 43, 2w^{3} - 5w^{2} - 6w + 4]$ $-\frac{8}{3}e^{5} + \frac{25}{3}e^{4} + \frac{94}{3}e^{3} - \frac{137}{3}e^{2} - 96e - \frac{52}{3}$
47 $[47, 47, -w^{3} + 2w^{2} + 5w - 1]$ $\phantom{-}e^{5} - 3e^{4} - 12e^{3} + 16e^{2} + 39e + 1$
53 $[53, 53, -w - 3]$ $-\frac{1}{3}e^{5} + \frac{2}{3}e^{4} + \frac{17}{3}e^{3} - \frac{13}{3}e^{2} - 22e - \frac{11}{3}$
53 $[53, 53, -w^{3} + 3w^{2} + 3w - 6]$ $\phantom{-}e^{5} - 3e^{4} - 12e^{3} + 15e^{2} + 38e + 12$
59 $[59, 59, 2w^{2} - 3w - 6]$ $\phantom{-}\frac{8}{3}e^{5} - \frac{28}{3}e^{4} - \frac{82}{3}e^{3} + \frac{161}{3}e^{2} + 71e + \frac{7}{3}$
59 $[59, 59, w^{3} - w^{2} - 7w - 3]$ $-\frac{1}{3}e^{5} + \frac{5}{3}e^{4} + \frac{5}{3}e^{3} - \frac{34}{3}e^{2} + \frac{7}{3}$
79 $[79, 79, 2w^{3} - 4w^{2} - 8w + 3]$ $\phantom{-}\frac{5}{3}e^{5} - \frac{16}{3}e^{4} - \frac{55}{3}e^{3} + \frac{83}{3}e^{2} + 52e + \frac{31}{3}$
79 $[79, 79, w^{2} - 2w - 1]$ $\phantom{-}\frac{11}{3}e^{5} - \frac{37}{3}e^{4} - \frac{115}{3}e^{3} + \frac{197}{3}e^{2} + 106e + \frac{61}{3}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, -w^{3} + 2w^{2} + 5w - 3]$ $-1$
$5$ $[5, 5, w]$ $1$