Properties

Base field \(\Q(\sqrt{201}) \)
Weight [2, 2]
Level norm 32
Level $[32, 16, -2w + 14]$
Label 2.2.201.1-32.3-h
Dimension 3
CM no
Base change no

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Base field \(\Q(\sqrt{201}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 50\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[32, 16, -2w + 14]$
Label 2.2.201.1-32.3-h
Dimension 3
Is CM no
Is base change no
Parent newspace dimension 48

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{3} \) \(\mathstrut -\mathstrut x^{2} \) \(\mathstrut -\mathstrut 4x \) \(\mathstrut +\mathstrut 3\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 112]$ $-1$
2 $[2, 2, -17w + 129]$ $\phantom{-}0$
3 $[3, 3, -124w + 941]$ $\phantom{-}e$
5 $[5, 5, -2w + 15]$ $\phantom{-}e^{2} - e - 3$
5 $[5, 5, -2w - 13]$ $-e^{2} + e + 3$
11 $[11, 11, 12w + 79]$ $\phantom{-}e^{2} + 2e - 6$
11 $[11, 11, -12w + 91]$ $\phantom{-}e^{2} + 2e - 6$
19 $[19, 19, -90w - 593]$ $-2e^{2} + 2e + 6$
19 $[19, 19, 90w - 683]$ $\phantom{-}2e^{2} - 2e - 6$
37 $[37, 37, -4w - 27]$ $-4e^{2} - 2e + 12$
37 $[37, 37, -4w + 31]$ $-4e^{2} - 2e + 12$
41 $[41, 41, 158w + 1041]$ $-6$
41 $[41, 41, 158w - 1199]$ $\phantom{-}6$
49 $[49, 7, -7]$ $-4e^{2} + 4e + 10$
53 $[53, 53, 46w - 349]$ $-3e - 6$
53 $[53, 53, 46w + 303]$ $\phantom{-}3e + 6$
67 $[67, 67, 586w - 4447]$ $\phantom{-}0$
73 $[73, 73, -32w - 211]$ $\phantom{-}e^{2} - 4e - 6$
73 $[73, 73, 32w - 243]$ $\phantom{-}e^{2} - 4e - 6$
101 $[101, 101, 2w - 11]$ $-4e^{2} - 5e + 18$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -17w - 112]$ $1$
2 $[2, 2, -17w + 129]$ $-1$