Properties

Base field 4.4.8768.1
Weight [2, 2, 2, 2]
Level norm 31
Level $[31, 31, w^{2} - 5]$
Label 4.4.8768.1-31.1-b
Dimension 6
CM no
Base change no

Related objects

Downloads

Learn more about

Base field 4.4.8768.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 5x^{2} + 6x + 7\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[31, 31, w^{2} - 5]$
Label 4.4.8768.1-31.1-b
Dimension 6
Is CM no
Is base change no
Parent newspace dimension 23

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{6} \) \(\mathstrut +\mathstrut 5x^{5} \) \(\mathstrut -\mathstrut 2x^{4} \) \(\mathstrut -\mathstrut 42x^{3} \) \(\mathstrut -\mathstrut 52x^{2} \) \(\mathstrut +\mathstrut 22x \) \(\mathstrut +\mathstrut 45\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -w^{2} + w + 3]$ $\phantom{-}e$
7 $[7, 7, w]$ $\phantom{-}2e^{5} + 7e^{4} - 15e^{3} - 62e^{2} - 7e + 58$
7 $[7, 7, -w^{2} + 2w + 1]$ $\phantom{-}2e^{5} + 6e^{4} - 16e^{3} - 53e^{2} + 48$
7 $[7, 7, w^{2} - 2]$ $-6e^{5} - 20e^{4} + 45e^{3} + 177e^{2} + 20e - 167$
7 $[7, 7, w - 1]$ $\phantom{-}5e^{5} + 17e^{4} - 37e^{3} - 150e^{2} - 21e + 138$
23 $[23, 23, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}4e^{5} + 13e^{4} - 30e^{3} - 113e^{2} - 13e + 99$
23 $[23, 23, w^{3} - 2w^{2} - 2w + 2]$ $\phantom{-}3e^{5} + 10e^{4} - 23e^{3} - 89e^{2} - 6e + 84$
31 $[31, 31, w^{2} - 5]$ $\phantom{-}1$
31 $[31, 31, -w^{2} + 2w + 4]$ $\phantom{-}4e^{5} + 13e^{4} - 30e^{3} - 115e^{2} - 15e + 107$
41 $[41, 41, -w^{3} + 2w^{2} + 2w - 6]$ $-4e^{5} - 15e^{4} + 28e^{3} + 133e^{2} + 27e - 128$
41 $[41, 41, w^{3} - w^{2} - 3w - 3]$ $-2e^{2} + e + 12$
47 $[47, 47, w^{2} - 2w - 5]$ $-12e^{5} - 41e^{4} + 89e^{3} + 364e^{2} + 49e - 342$
47 $[47, 47, w^{2} - 6]$ $\phantom{-}4e^{5} + 12e^{4} - 31e^{3} - 105e^{2} - 8e + 88$
71 $[71, 71, -w^{3} + 2w^{2} + 3w - 1]$ $\phantom{-}13e^{5} + 45e^{4} - 96e^{3} - 400e^{2} - 51e + 387$
71 $[71, 71, -w^{3} + w^{2} + 4w - 3]$ $-12e^{5} - 41e^{4} + 89e^{3} + 363e^{2} + 51e - 343$
79 $[79, 79, -w - 3]$ $\phantom{-}9e^{5} + 32e^{4} - 66e^{3} - 285e^{2} - 44e + 270$
79 $[79, 79, w - 4]$ $\phantom{-}5e^{5} + 18e^{4} - 35e^{3} - 159e^{2} - 33e + 140$
81 $[81, 3, -3]$ $\phantom{-}3e^{5} + 11e^{4} - 21e^{3} - 101e^{2} - 22e + 107$
89 $[89, 89, w^{2} - 3w - 2]$ $\phantom{-}7e^{5} + 25e^{4} - 50e^{3} - 223e^{2} - 40e + 210$
89 $[89, 89, w^{2} + w - 4]$ $-7e^{5} - 22e^{4} + 55e^{3} + 192e^{2} + 9e - 165$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31, 31, w^{2} - 5]$ $-1$