Properties

Base field \(\Q(\sqrt{13}) \)
Weight [2, 2]
Level norm 121
Level $[121, 11, -11]$
Label 2.2.13.1-121.1-a
Dimension 1
CM no
Base change yes

Related objects

Downloads

Learn more about

Base field \(\Q(\sqrt{13}) \)

Generator \(w\), with minimal polynomial \(x^{2} - x - 3\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2]
Level $[121, 11, -11]$
Label 2.2.13.1-121.1-a
Dimension 1
Is CM no
Is base change yes
Parent newspace dimension 11

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, -w]$ $-1$
3 $[3, 3, -w + 1]$ $-1$
4 $[4, 2, 2]$ $\phantom{-}0$
13 $[13, 13, -2w + 1]$ $\phantom{-}4$
17 $[17, 17, w + 4]$ $-2$
17 $[17, 17, -w + 5]$ $-2$
23 $[23, 23, 3w + 1]$ $-1$
23 $[23, 23, -3w + 4]$ $-1$
25 $[25, 5, 5]$ $-9$
29 $[29, 29, 3w - 2]$ $\phantom{-}0$
29 $[29, 29, -3w + 1]$ $\phantom{-}0$
43 $[43, 43, -4w - 1]$ $-6$
43 $[43, 43, 4w - 5]$ $-6$
49 $[49, 7, -7]$ $-10$
53 $[53, 53, -w - 7]$ $-6$
53 $[53, 53, w - 8]$ $-6$
61 $[61, 61, -3w - 8]$ $\phantom{-}12$
61 $[61, 61, 3w - 11]$ $\phantom{-}12$
79 $[79, 79, 5w - 4]$ $-10$
79 $[79, 79, 5w - 1]$ $-10$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
121 $[121, 11, -11]$ $-1$