Properties

Label 3.3.1425.1-15.1-c
Base field 3.3.1425.1
Weight $[2, 2, 2]$
Level norm $15$
Level $[15, 15, w + 3]$
Dimension $3$
CM no
Base change no

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Base field 3.3.1425.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 8x - 3\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[15, 15, w + 3]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $17$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} - 7x - 2\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $-1$
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 7]$ $-1$
8 $[8, 2, 2]$ $-\frac{1}{2}e^{2} + \frac{1}{2}e + 1$
11 $[11, 11, w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{3}{2}e - 1$
13 $[13, 13, w^{2} - 2w - 8]$ $-\frac{1}{2}e^{2} - \frac{1}{2}e$
17 $[17, 17, w^{2} - 2w - 7]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 3$
19 $[19, 19, -w^{2} + 2w + 4]$ $-\frac{3}{2}e^{2} + \frac{3}{2}e + 6$
19 $[19, 19, -2w^{2} + 3w + 16]$ $-\frac{1}{2}e^{2} + \frac{3}{2}e + 4$
23 $[23, 23, -w^{2} + 2w + 2]$ $\phantom{-}\frac{1}{2}e^{2} + \frac{1}{2}e - 3$
31 $[31, 31, 2w^{2} - 3w - 13]$ $\phantom{-}2e^{2} - e - 7$
37 $[37, 37, w^{2} - w - 10]$ $-\frac{1}{2}e^{2} - \frac{3}{2}e + 3$
43 $[43, 43, 3w^{2} - 5w - 19]$ $-e - 5$
43 $[43, 43, w^{2} - w - 4]$ $\phantom{-}2e + 1$
43 $[43, 43, 2w^{2} - 2w - 17]$ $\phantom{-}e^{2} + e - 11$
47 $[47, 47, w^{2} - 2]$ $-2$
67 $[67, 67, w^{2} - 3w - 5]$ $\phantom{-}\frac{3}{2}e^{2} - \frac{3}{2}e - 12$
79 $[79, 79, -w^{2} + 3w - 1]$ $-\frac{1}{2}e^{2} - \frac{5}{2}e + 3$
83 $[83, 83, w^{2} + w - 4]$ $-e^{2} + 2e + 10$
97 $[97, 97, w^{2} - 11]$ $-\frac{3}{2}e^{2} + \frac{1}{2}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$
$5$ $[5, 5, w^{2} - w - 7]$ $1$