Properties

Label 2.2.305.1-4.2-b
Base field \(\Q(\sqrt{305}) \)
Weight $[2, 2]$
Level norm $4$
Level $[4, 4, -w - 8]$
Dimension $10$
CM no
Base change no

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Base field \(\Q(\sqrt{305}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 76\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[4, 4, -w - 8]$
Dimension: $10$
CM: no
Base change: no
Newspace dimension: $20$

Hecke eigenvalues ($q$-expansion)

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

\(x^{10} + 12x^{8} + 46x^{6} + 61x^{4} + 25x^{2} + 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
2 $[2, 2, w + 1]$ $\phantom{-}e$
5 $[5, 5, -4w + 37]$ $-e^{8} - 12e^{6} - 45e^{4} - 53e^{2} - 12$
7 $[7, 7, w + 2]$ $\phantom{-}3e^{9} + 35e^{7} + 127e^{5} + 146e^{3} + 36e$
7 $[7, 7, w + 4]$ $-e$
9 $[9, 3, 3]$ $-e^{8} - 12e^{6} - 45e^{4} - 54e^{2} - 14$
17 $[17, 17, w + 6]$ $-2e^{9} - 23e^{7} - 81e^{5} - 86e^{3} - 18e$
17 $[17, 17, w + 10]$ $\phantom{-}4e^{9} + 47e^{7} + 171e^{5} + 192e^{3} + 38e$
19 $[19, 19, -2w + 19]$ $\phantom{-}e^{6} + 9e^{4} + 22e^{2} + 10$
19 $[19, 19, -2w - 17]$ $\phantom{-}2e^{8} + 23e^{6} + 81e^{4} + 86e^{2} + 16$
23 $[23, 23, w + 5]$ $-7e^{9} - 82e^{7} - 298e^{5} - 339e^{3} - 79e$
23 $[23, 23, w + 17]$ $-2e^{9} - 23e^{7} - 81e^{5} - 87e^{3} - 20e$
37 $[37, 37, w + 1]$ $-4e^{9} - 47e^{7} - 172e^{5} - 200e^{3} - 51e$
37 $[37, 37, w + 35]$ $-4e^{9} - 47e^{7} - 172e^{5} - 202e^{3} - 59e$
41 $[41, 41, -22w + 203]$ $-4e^{8} - 47e^{6} - 173e^{4} - 204e^{2} - 45$
41 $[41, 41, -6w + 55]$ $\phantom{-}e^{6} + 11e^{4} + 32e^{2} + 15$
43 $[43, 43, w + 20]$ $\phantom{-}2e^{9} + 23e^{7} + 80e^{5} + 78e^{3} + 3e$
43 $[43, 43, w + 22]$ $\phantom{-}6e^{9} + 71e^{7} + 262e^{5} + 306e^{3} + 69e$
53 $[53, 53, w + 13]$ $-e^{9} - 12e^{7} - 47e^{5} - 66e^{3} - 26e$
53 $[53, 53, w + 39]$ $\phantom{-}3e^{9} + 34e^{7} + 117e^{5} + 118e^{3} + 20e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$2$ $[2, 2, w]$ $1$