# Properties

 Label 4.4.17609.1-17.1-a Base field 4.4.17609.1 Weight $[2, 2, 2, 2]$ Level norm $17$ Level $[17, 17, w^{3} + w^{2} - 6w - 1]$ Dimension $14$ CM no Base change no

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## Base field 4.4.17609.1

Generator $$w$$, with minimal polynomial $$x^{4} - x^{3} - 7x^{2} + 10x - 1$$; narrow class number $$2$$ and class number $$1$$.

## Form

 Weight: $[2, 2, 2, 2]$ Level: $[17, 17, w^{3} + w^{2} - 6w - 1]$ Dimension: $14$ CM: no Base change: no Newspace dimension: $46$

## Hecke eigenvalues ($q$-expansion)

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

 $$x^{14} - 16x^{12} + 101x^{10} - 318x^{8} + 519x^{6} - 411x^{4} + 124x^{2} - 1$$
Norm Prime Eigenvalue
2 $[2, 2, -w + 1]$ $\phantom{-}e$
5 $[5, 5, w^{3} + w^{2} - 4w + 1]$ $-e^{10} + 11e^{8} - 42e^{6} + 65e^{4} - 36e^{2} + 2$
7 $[7, 7, -w^{3} + 6w - 2]$ $-e^{11} + 12e^{9} - 51e^{7} + 90e^{5} - 57e^{3} + 5e$
8 $[8, 2, w^{3} - 7w + 3]$ $\phantom{-}e^{11} - 12e^{9} + 52e^{7} - 98e^{5} + 77e^{3} - 21e$
11 $[11, 11, -w^{3} + 6w - 4]$ $\phantom{-}e^{13} - 15e^{11} + 87e^{9} - 244e^{7} + 338e^{5} - 212e^{3} + 47e$
17 $[17, 17, w^{3} + w^{2} - 6w - 1]$ $\phantom{-}1$
17 $[17, 17, -w^{2} - w + 3]$ $-e^{13} + 15e^{11} - 87e^{9} + 243e^{7} - 330e^{5} + 192e^{3} - 32e$
31 $[31, 31, 2w^{3} + w^{2} - 13w + 3]$ $-e^{11} + 11e^{9} - 43e^{7} + 73e^{5} - 55e^{3} + 16e$
37 $[37, 37, -3w^{3} - w^{2} + 18w - 3]$ $-e^{13} + 15e^{11} - 87e^{9} + 243e^{7} - 326e^{5} + 171e^{3} - 12e$
41 $[41, 41, w^{2} + 2w - 4]$ $\phantom{-}e^{13} - 12e^{11} + 49e^{9} - 63e^{7} - 68e^{5} + 223e^{3} - 130e$
47 $[47, 47, 2w^{3} + 2w^{2} - 11w - 2]$ $-e^{12} + 16e^{10} - 96e^{8} + 267e^{6} - 338e^{4} + 151e^{2} - 2$
47 $[47, 47, -3w^{3} - w^{2} + 19w - 6]$ $-e^{13} + 13e^{11} - 62e^{9} + 128e^{7} - 91e^{5} - 32e^{3} + 48e$
59 $[59, 59, -2w^{3} + 13w - 6]$ $\phantom{-}e^{13} - 13e^{11} + 64e^{9} - 151e^{7} + 181e^{5} - 108e^{3} + 27e$
59 $[59, 59, -w^{3} - w^{2} + 5w + 2]$ $\phantom{-}e^{12} - 15e^{10} + 86e^{8} - 232e^{6} + 284e^{4} - 111e^{2} - 12$
59 $[59, 59, w^{2} + w - 1]$ $-2e^{11} + 26e^{9} - 127e^{7} + 282e^{5} - 265e^{3} + 71e$
59 $[59, 59, w^{2} + 2w - 6]$ $\phantom{-}2e^{12} - 23e^{10} + 94e^{8} - 165e^{6} + 127e^{4} - 51e^{2} + 10$
61 $[61, 61, -w^{3} + w^{2} + 8w - 7]$ $\phantom{-}2e^{13} - 29e^{11} + 163e^{9} - 446e^{7} + 608e^{5} - 372e^{3} + 75e$
67 $[67, 67, w^{3} + 2w^{2} - 4w - 4]$ $-e^{12} + 10e^{10} - 29e^{8} + 7e^{6} + 60e^{4} - 28e^{2} - 12$
73 $[73, 73, -2w^{3} - w^{2} + 12w - 4]$ $-e^{13} + 16e^{11} - 95e^{9} + 253e^{7} - 275e^{5} + 45e^{3} + 55e$
81 $[81, 3, -3]$ $\phantom{-}2e^{10} - 22e^{8} + 86e^{6} - 141e^{4} + 82e^{2} - 5$
 Display number of eigenvalues

## Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$17$ $[17, 17, w^{3} + w^{2} - 6w - 1]$ $-1$