Base field \(\Q(\sqrt{103}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 103\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[3,3,w - 10]$ |
| Dimension: | $1$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $28$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q$.
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, 47w - 477]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w - 10]$ | $\phantom{-}1$ |
| 3 | $[3, 3, -w + 10]$ | $-1$ |
| 11 | $[11, 11, 27w + 274]$ | $-2$ |
| 11 | $[11, 11, 27w - 274]$ | $\phantom{-}3$ |
| 13 | $[13, 13, 6w - 61]$ | $\phantom{-}3$ |
| 13 | $[13, 13, 6w + 61]$ | $-2$ |
| 17 | $[17, 17, 13w + 132]$ | $-4$ |
| 17 | $[17, 17, 13w - 132]$ | $\phantom{-}1$ |
| 25 | $[25, 5, -5]$ | $-2$ |
| 29 | $[29, 29, -2w + 21]$ | $\phantom{-}1$ |
| 29 | $[29, 29, -2w - 21]$ | $\phantom{-}6$ |
| 31 | $[31, 31, -8w - 81]$ | $\phantom{-}2$ |
| 31 | $[31, 31, -8w + 81]$ | $-8$ |
| 41 | $[41, 41, -w - 12]$ | $-12$ |
| 41 | $[41, 41, w - 12]$ | $\phantom{-}3$ |
| 43 | $[43, 43, -34w - 345]$ | $-9$ |
| 43 | $[43, 43, -34w + 345]$ | $\phantom{-}11$ |
| 47 | $[47, 47, 168w - 1705]$ | $-2$ |
| 47 | $[47, 47, -309w + 3136]$ | $-7$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $3$ | $[3,3,w - 10]$ | $1$ |