Properties

Base field \(\Q(\sqrt{93}) \)
Weight [2, 2]
Level norm 147
Level $[147, 21, -7w + 35]$
Label 2.2.93.1-147.1-j
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{93}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 23\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2]
Level $[147, 21, -7w + 35]$
Label 2.2.93.1-147.1-j
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 106

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w + 5]$ $-1$
4 $[4, 2, 2]$ $-3$
7 $[7, 7, w - 6]$ $-1$
7 $[7, 7, -w - 5]$ $-1$
11 $[11, 11, -w - 3]$ $-4$
11 $[11, 11, w - 4]$ $-4$
17 $[17, 17, w + 2]$ $\phantom{-}6$
17 $[17, 17, w - 3]$ $\phantom{-}6$
19 $[19, 19, w + 6]$ $\phantom{-}4$
19 $[19, 19, -w + 7]$ $\phantom{-}4$
23 $[23, 23, w]$ $\phantom{-}0$
23 $[23, 23, w - 1]$ $\phantom{-}0$
25 $[25, 5, -5]$ $-6$
29 $[29, 29, -2w + 9]$ $\phantom{-}2$
29 $[29, 29, 2w + 7]$ $\phantom{-}2$
31 $[31, 31, 3w - 17]$ $\phantom{-}0$
53 $[53, 53, 3w - 14]$ $-6$
53 $[53, 53, -3w - 11]$ $-6$
67 $[67, 67, -w - 9]$ $\phantom{-}4$
67 $[67, 67, w - 10]$ $\phantom{-}4$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, -w + 5]$ $1$
7 $[7, 7, w - 6]$ $1$
7 $[7, 7, -w - 5]$ $1$