Properties

Label 3.3.1425.1-9.3-g
Base field 3.3.1425.1
Weight $[2, 2, 2]$
Level norm $9$
Level $[9, 9, -w^{2} + w + 6]$
Dimension $4$
CM no
Base change no

Related objects

Downloads

Learn more

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: $[9, 9, -w^{2} + w + 6]$
Dimension: $4$
CM: no
Base change: no
Newspace dimension: $13$

Hecke eigenvalues ($q$-expansion)

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

\(x^{4} - 9x^{2} + 15\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{2} - w - 7]$ $-e$
8 $[8, 2, 2]$ $-e^{3} + 5e$
11 $[11, 11, w - 1]$ $\phantom{-}e^{3} - 5e$
13 $[13, 13, w^{2} - 2w - 8]$ $\phantom{-}0$
17 $[17, 17, w^{2} - 2w - 7]$ $\phantom{-}e^{3} - 6e$
19 $[19, 19, -w^{2} + 2w + 4]$ $\phantom{-}2e^{2} - 11$
19 $[19, 19, -2w^{2} + 3w + 16]$ $-2e^{2} + 6$
23 $[23, 23, -w^{2} + 2w + 2]$ $-e^{3} + 6e$
31 $[31, 31, 2w^{2} - 3w - 13]$ $-e^{2} - 3$
37 $[37, 37, w^{2} - w - 10]$ $\phantom{-}2e^{2} - 15$
43 $[43, 43, 3w^{2} - 5w - 19]$ $-2e^{2} + 15$
43 $[43, 43, w^{2} - w - 4]$ $-4e^{2} + 15$
43 $[43, 43, 2w^{2} - 2w - 17]$ $-2e^{2} + 5$
47 $[47, 47, w^{2} - 2]$ $\phantom{-}3e$
67 $[67, 67, w^{2} - 3w - 5]$ $\phantom{-}2e^{2} - 5$
79 $[79, 79, -w^{2} + 3w - 1]$ $\phantom{-}4e^{2} - 21$
83 $[83, 83, w^{2} + w - 4]$ $\phantom{-}e^{3} - 12e$
97 $[97, 97, w^{2} - 11]$ $-e^{2} - 5$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w]$ $1$