# Properties

 Label 3.3.1492.1-14.3-d Base field 3.3.1492.1 Weight $[2, 2, 2]$ Level norm $14$ Level $[14, 14, w - 1]$ Dimension $3$ CM no Base change no

# Related objects

• L-function not available

## Base field 3.3.1492.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 9x - 5$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2]$ Level: $[14, 14, w - 1]$ Dimension: $3$ 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:

 $$x^{3} + 3x^{2} - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w - 1]$ $\phantom{-}1$
5 $[5, 5, w]$ $\phantom{-}e$
7 $[7, 7, w^{2} - 2w - 8]$ $-e^{2} - 4e$
7 $[7, 7, -2w^{2} + 3w + 16]$ $\phantom{-}2e^{2} + 4e - 3$
7 $[7, 7, -w^{2} + 2w + 6]$ $\phantom{-}1$
11 $[11, 11, w^{2} - 2w - 2]$ $-e^{2} - 3e - 2$
19 $[19, 19, -w + 2]$ $-5e^{2} - 12e$
23 $[23, 23, -w^{2} + 3w + 1]$ $\phantom{-}2e^{2} + 6e + 1$
25 $[25, 5, w^{2} - w - 9]$ $\phantom{-}2e^{2} + 9e + 2$
27 $[27, 3, 3]$ $\phantom{-}2e - 1$
29 $[29, 29, -w^{2} - w + 1]$ $\phantom{-}2e^{2} + 5e - 4$
29 $[29, 29, w^{2} - 2w - 4]$ $\phantom{-}2e^{2} + 5e - 4$
29 $[29, 29, -w^{2} + w + 11]$ $-2e^{2} - 3e + 1$
43 $[43, 43, 2w^{2} - 3w - 18]$ $-2e^{2} - e + 3$
47 $[47, 47, -2w + 7]$ $\phantom{-}e^{2} + 5e - 1$
53 $[53, 53, w^{2} - w - 3]$ $-3e^{2} - 12e - 4$
61 $[61, 61, w^{2} + 2w + 2]$ $\phantom{-}7e^{2} + 15e - 8$
67 $[67, 67, -2w^{2} + 5w + 8]$ $-6e^{2} - 15e$
79 $[79, 79, w^{2} - 3w - 9]$ $\phantom{-}10e^{2} + 22e - 4$
97 $[97, 97, -w^{2} - 2w + 2]$ $-e^{2} - 7e - 11$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, -w - 1]$ $-1$
$7$ $[7, 7, -w^{2} + 2w + 6]$ $-1$