Properties

Label 3.3.1593.1-15.1-d
Base field 3.3.1593.1
Weight $[2, 2, 2]$
Level norm $15$
Level $[15, 15, w - 1]$
Dimension $6$
CM no
Base change no

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Base field 3.3.1593.1

Generator \(w\), with minimal polynomial \(x^{3} - 9x - 7\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[15, 15, w - 1]$
Dimension: $6$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

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

\(x^{6} + 11x^{5} + 38x^{4} + 28x^{3} - 67x^{2} - 59x + 52\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w + 2]$ $-1$
5 $[5, 5, w^{2} - 2w - 4]$ $-1$
7 $[7, 7, w]$ $\phantom{-}e$
7 $[7, 7, w + 3]$ $-e^{2} - 4e$
7 $[7, 7, -w^{2} + 2w + 3]$ $\phantom{-}e^{3} + 6e^{2} + 6e - 8$
8 $[8, 2, 2]$ $-\frac{1}{2}e^{4} - \frac{7}{2}e^{3} - \frac{11}{2}e^{2} + \frac{3}{2}e + 3$
13 $[13, 13, w^{2} - 3w - 2]$ $-\frac{1}{2}e^{4} - \frac{9}{2}e^{3} - \frac{21}{2}e^{2} - \frac{1}{2}e + 8$
17 $[17, 17, w - 2]$ $-\frac{1}{2}e^{5} - \frac{9}{2}e^{4} - \frac{21}{2}e^{3} + \frac{5}{2}e^{2} + 18e - 6$
25 $[25, 5, -w^{2} - w + 3]$ $\phantom{-}e^{5} + 8e^{4} + 13e^{3} - 22e^{2} - 36e + 30$
29 $[29, 29, w^{2} - 2w - 6]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{7}{2}e^{3} + \frac{9}{2}e^{2} - \frac{7}{2}e$
31 $[31, 31, w^{2} - 5]$ $-e^{5} - 8e^{4} - 13e^{3} + 20e^{2} + 30e - 28$
37 $[37, 37, -w^{2} - 2w + 2]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{9}{2}e^{3} + \frac{25}{2}e^{2} + \frac{13}{2}e - 16$
41 $[41, 41, w^{2} - 8]$ $\phantom{-}\frac{3}{2}e^{5} + \frac{25}{2}e^{4} + \frac{47}{2}e^{3} - \frac{49}{2}e^{2} - 54e + 34$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}\frac{1}{2}e^{4} + \frac{7}{2}e^{3} + \frac{13}{2}e^{2} + \frac{5}{2}e - 2$
53 $[53, 53, 2w^{2} - 5w - 4]$ $\phantom{-}2e + 6$
59 $[59, 59, w^{2} - 3]$ $-\frac{1}{2}e^{5} - \frac{5}{2}e^{4} + \frac{9}{2}e^{3} + \frac{57}{2}e^{2} + 7e - 28$
59 $[59, 59, w^{2} - 3w - 5]$ $-e^{5} - \frac{15}{2}e^{4} - \frac{19}{2}e^{3} + \frac{57}{2}e^{2} + \frac{77}{2}e - 34$
61 $[61, 61, -w^{2} + 2w + 12]$ $-\frac{1}{2}e^{5} - \frac{11}{2}e^{4} - \frac{39}{2}e^{3} - \frac{39}{2}e^{2} + 13e + 18$
67 $[67, 67, -2w^{2} + 6w + 3]$ $-e^{5} - \frac{17}{2}e^{4} - \frac{37}{2}e^{3} + \frac{3}{2}e^{2} + \frac{41}{2}e + 2$
71 $[71, 71, w^{2} - w - 11]$ $\phantom{-}e^{5} + 9e^{4} + 20e^{3} - 9e^{2} - 33e + 20$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 2]$ $1$
$5$ $[5, 5, w^{2} - 2w - 4]$ $1$