Properties

Label 4.4.16357.1-15.2-d
Base field 4.4.16357.1
Weight $[2, 2, 2, 2]$
Level norm $15$
Level $[15, 15, -w^{3} + 6w - 1]$
Dimension $1$
CM no
Base change no

Related objects

Downloads

Learn more

Base field 4.4.16357.1

Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - x + 1\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2, 2]$
Level: $[15, 15, -w^{3} + 6w - 1]$
Dimension: $1$
CM: no
Base change: no
Newspace dimension: $18$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q$.
Norm Prime Eigenvalue
3 $[3, 3, w + 1]$ $-1$
5 $[5, 5, -w^{3} + 5w + 2]$ $\phantom{-}1$
5 $[5, 5, w - 1]$ $\phantom{-}0$
11 $[11, 11, -w^{3} + 5w]$ $\phantom{-}0$
13 $[13, 13, -w^{3} + w^{2} + 6w - 3]$ $-4$
16 $[16, 2, 2]$ $-5$
19 $[19, 19, 2w^{3} - w^{2} - 11w + 2]$ $\phantom{-}4$
25 $[25, 5, -w^{2} + w + 3]$ $-4$
27 $[27, 3, w^{3} - w^{2} - 5w + 4]$ $-4$
31 $[31, 31, -w - 3]$ $-2$
37 $[37, 37, -w^{3} - w^{2} + 6w + 4]$ $\phantom{-}2$
41 $[41, 41, w^{3} + w^{2} - 6w - 5]$ $\phantom{-}6$
43 $[43, 43, w^{3} - 7w - 2]$ $-4$
47 $[47, 47, -2w^{3} + 11w + 2]$ $\phantom{-}6$
61 $[61, 61, w^{2} - 3]$ $\phantom{-}4$
67 $[67, 67, w^{2} + w - 4]$ $\phantom{-}4$
79 $[79, 79, -4w^{3} + 2w^{2} + 22w - 9]$ $\phantom{-}4$
97 $[97, 97, -3w^{3} + 2w^{2} + 19w - 6]$ $-8$
97 $[97, 97, -w^{3} + 6w - 3]$ $-2$
97 $[97, 97, -3w^{3} + 16w]$ $\phantom{-}14$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$3$ $[3, 3, w + 1]$ $1$
$5$ $[5, 5, -w^{3} + 5w + 2]$ $-1$