# Properties

 Label 3.3.316.1-37.1-c Base field 3.3.316.1 Weight $[2, 2, 2]$ Level norm $37$ Level $[37, 37, 2w^{2} - 2w - 5]$ Dimension $4$ CM no Base change no

# Related objects

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## Base field 3.3.316.1

Generator $$w$$, with minimal polynomial $$x^{3} - x^{2} - 4x + 2$$; narrow class number $$1$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2]$ Level: $[37, 37, 2w^{2} - 2w - 5]$ Dimension: $4$ CM: no Base change: no Newspace dimension: $11$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{4} + 2x^{3} - 2x^{2} - 3x + 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w]$ $\phantom{-}e$
2 $[2, 2, w - 1]$ $\phantom{-}e^{3} + e^{2} - 2e - 1$
11 $[11, 11, w^{2} - w - 1]$ $\phantom{-}e^{3} + 4e^{2} - 6$
17 $[17, 17, -w^{2} - w + 3]$ $-3e^{3} - 7e^{2} + 5e + 6$
19 $[19, 19, w^{2} - w + 1]$ $-3e - 3$
23 $[23, 23, 2w - 3]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 4$
27 $[27, 3, 3]$ $\phantom{-}e^{3} + 4e^{2} + 3e - 7$
29 $[29, 29, 2w + 1]$ $-4e^{2} - 6e + 5$
31 $[31, 31, 2w^{2} - 2w - 9]$ $\phantom{-}e^{2} + 2e - 3$
37 $[37, 37, 2w^{2} - 2w - 5]$ $-1$
41 $[41, 41, 2w^{2} - 9]$ $\phantom{-}3e^{3} + 5e^{2} - 4e - 8$
43 $[43, 43, w^{2} + w - 5]$ $-3e^{3} - 7e^{2} + 4e + 2$
43 $[43, 43, -3w^{2} + w + 15]$ $\phantom{-}e^{3} - 2e^{2} - 5e + 1$
43 $[43, 43, -2w^{2} + 2w + 11]$ $-4e^{3} - 2e^{2} + 8e - 3$
53 $[53, 53, w^{2} - w - 7]$ $-6e^{3} - 9e^{2} + 9e + 8$
61 $[61, 61, 4w^{2} - 2w - 15]$ $-3e^{3} - 5e^{2} + 2e + 2$
67 $[67, 67, -5w^{2} + 3w + 23]$ $\phantom{-}e^{3} + 4e^{2} + 2e - 11$
73 $[73, 73, 2w^{2} - 3]$ $\phantom{-}e^{3} - 4e^{2} - 4e + 5$
73 $[73, 73, -3w^{2} - w + 7]$ $\phantom{-}5e^{3} + 14e^{2} - 12$
73 $[73, 73, -6w^{2} + 4w + 25]$ $\phantom{-}e^{3} + 9e^{2} + 4e - 17$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$37$ $[37, 37, 2w^{2} - 2w - 5]$ $1$