Properties

Label 2.2.77.1-175.1-a
Base field \(\Q(\sqrt{77}) \)
Weight $[2, 2]$
Level norm $175$
Level $[175, 35, 5w + 15]$
Dimension $1$
CM no
Base change yes

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Base field \(\Q(\sqrt{77}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 19\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2]$
Level: $[175, 35, 5w + 15]$
Dimension: $1$
CM: no
Base change: yes
Newspace dimension: $142$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
4 $[4, 2, 2]$ $-4$
7 $[7, 7, -w - 3]$ $-1$
9 $[9, 3, 3]$ $-5$
11 $[11, 11, w + 5]$ $-3$
13 $[13, 13, w + 2]$ $-5$
13 $[13, 13, w - 3]$ $-5$
17 $[17, 17, w + 1]$ $-3$
17 $[17, 17, -w + 2]$ $-3$
19 $[19, 19, w]$ $-2$
19 $[19, 19, w - 1]$ $-2$
23 $[23, 23, w + 6]$ $-6$
23 $[23, 23, -w + 7]$ $-6$
25 $[25, 5, -5]$ $\phantom{-}1$
37 $[37, 37, -w - 7]$ $\phantom{-}2$
37 $[37, 37, w - 8]$ $\phantom{-}2$
41 $[41, 41, 2w - 7]$ $\phantom{-}12$
41 $[41, 41, -2w - 5]$ $\phantom{-}12$
53 $[53, 53, -w - 8]$ $\phantom{-}12$
53 $[53, 53, w - 9]$ $\phantom{-}12$
61 $[61, 61, 2w - 5]$ $-8$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w - 3]$ $1$
$25$ $[25, 5, -5]$ $-1$