Properties

Base field \(\Q(\sqrt{113}) \)
Weight [2, 2]
Level norm 4
Level $[4, 2, 2]$
Label 2.2.113.1-4.1-b
Dimension 1
CM no
Base change yes

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Base field \(\Q(\sqrt{113}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 28\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[4, 2, 2]$
Label 2.2.113.1-4.1-b
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 7

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $-1$
2 $[2, 2, w + 5]$ $-1$
7 $[7, 7, 6w - 35]$ $\phantom{-}2$
7 $[7, 7, -6w - 29]$ $\phantom{-}2$
9 $[9, 3, 3]$ $\phantom{-}4$
11 $[11, 11, 4w + 19]$ $\phantom{-}0$
11 $[11, 11, 4w - 23]$ $\phantom{-}0$
13 $[13, 13, -2w + 11]$ $\phantom{-}2$
13 $[13, 13, 2w + 9]$ $\phantom{-}2$
25 $[25, 5, -5]$ $\phantom{-}8$
31 $[31, 31, 2w - 13]$ $\phantom{-}2$
31 $[31, 31, -2w - 11]$ $\phantom{-}2$
41 $[41, 41, -8w - 39]$ $-6$
41 $[41, 41, 8w - 47]$ $-6$
53 $[53, 53, -26w - 125]$ $-6$
53 $[53, 53, 26w - 151]$ $-6$
61 $[61, 61, -14w + 81]$ $-10$
61 $[61, 61, -14w - 67]$ $-10$
83 $[83, 83, 2w - 15]$ $\phantom{-}0$
83 $[83, 83, -2w - 13]$ $\phantom{-}0$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -w + 6]$ $1$
2 $[2, 2, w + 5]$ $1$