Properties

Label 2.2.280.1-1.1-c
Base field \(\Q(\sqrt{70}) \)
Weight $[2, 2]$
Level norm $1$
Level $[1, 1, 1]$
Dimension $2$
CM yes
Base change no

Related objects

Downloads

Learn more

Base field \(\Q(\sqrt{70}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 70\); narrow class number \(4\) and class number \(2\).

Form

Weight: $[2, 2]$
Level: $[1, 1, 1]$
Dimension: $2$
CM: yes
Base change: no
Newspace dimension: $36$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{2} + 7\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, w]$ $\phantom{-}0$
3 $[3, 3, w + 1]$ $-e$
3 $[3, 3, w + 2]$ $\phantom{-}e$
5 $[5, 5, -3w + 25]$ $\phantom{-}0$
7 $[7, 7, w]$ $\phantom{-}0$
11 $[11, 11, w - 9]$ $\phantom{-}3$
11 $[11, 11, -w - 9]$ $\phantom{-}3$
17 $[17, 17, w + 6]$ $-3e$
17 $[17, 17, w + 11]$ $\phantom{-}3e$
23 $[23, 23, w + 1]$ $\phantom{-}0$
23 $[23, 23, w + 22]$ $\phantom{-}0$
31 $[31, 31, 4w - 33]$ $\phantom{-}0$
31 $[31, 31, 4w + 33]$ $\phantom{-}0$
37 $[37, 37, w + 12]$ $\phantom{-}0$
37 $[37, 37, w + 25]$ $\phantom{-}0$
53 $[53, 53, w + 21]$ $\phantom{-}0$
53 $[53, 53, w + 32]$ $\phantom{-}0$
61 $[61, 61, -w - 3]$ $\phantom{-}0$
61 $[61, 61, w - 3]$ $\phantom{-}0$
73 $[73, 73, w + 17]$ $-4e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

This form has no Atkin-Lehner eigenvalues since the level is \((1)\).