Properties

Label 3.3.1937.1-15.1-c
Base field 3.3.1937.1
Weight $[2, 2, 2]$
Level norm $15$
Level $[15, 15, -w + 4]$
Dimension $3$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 3.3.1937.1

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

Form

Weight: $[2, 2, 2]$
Level: $[15, 15, -w + 4]$
Dimension: $3$
CM: no
Base change: no
Newspace dimension: $26$

Hecke eigenvalues ($q$-expansion)

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

\(x^{3} + 3x^{2} - 4x + 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w - 2]$ $-1$
5 $[5, 5, w + 1]$ $-1$
7 $[7, 7, w - 3]$ $\phantom{-}e$
8 $[8, 2, 2]$ $-2e^{2} - 6e + 4$
9 $[9, 3, w^{2} - 3w - 2]$ $-3e^{2} - 11e + 7$
13 $[13, 13, w + 3]$ $-2e^{2} - 8e$
13 $[13, 13, -w + 2]$ $-4e^{2} - 15e + 6$
19 $[19, 19, -w^{2} + 2w + 4]$ $-6e^{2} - 22e + 14$
23 $[23, 23, w^{2} - 4w + 1]$ $\phantom{-}4e^{2} + 12e - 10$
25 $[25, 5, w^{2} - 2w - 1]$ $-e - 4$
31 $[31, 31, w^{2} - 2w - 9]$ $\phantom{-}2e^{2} + 8e - 4$
37 $[37, 37, -w^{2} + 3w + 3]$ $-3e^{2} - 9e + 15$
41 $[41, 41, w^{2} - w - 1]$ $\phantom{-}13e^{2} + 46e - 28$
41 $[41, 41, w^{2} - w - 5]$ $\phantom{-}7e^{2} + 26e - 18$
41 $[41, 41, w^{2} - w - 10]$ $\phantom{-}12e^{2} + 42e - 28$
43 $[43, 43, -2w - 3]$ $\phantom{-}4e^{2} + 16e - 8$
47 $[47, 47, -w^{2} - w + 4]$ $-3e^{2} - 8e + 12$
49 $[49, 7, -w^{2} + 5w - 5]$ $\phantom{-}6e^{2} + 22e - 14$
59 $[59, 59, w^{2} - w - 4]$ $-2e^{2} - 6e + 4$
59 $[59, 59, w^{2} - 3]$ $-e^{2} - 3e + 9$
Display number of eigenvalues

Atkin-Lehner eigenvalues

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