Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 31
Level $[31,31,-2w^{2} + 3w + 11]$
Label 4.4.17725.1-31.2-b
Dimension 33
CM no
Base change no

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Base field 4.4.17725.1

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 12x^{2} + 13x + 41\); narrow class number \(1\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[31,31,-2w^{2} + 3w + 11]$
Label 4.4.17725.1-31.2-b
Dimension 33
Is CM no
Is base change no
Parent newspace dimension 59

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{33} \) \(\mathstrut -\mathstrut 14x^{32} \) \(\mathstrut -\mathstrut 81x^{31} \) \(\mathstrut +\mathstrut 1973x^{30} \) \(\mathstrut -\mathstrut 637x^{29} \) \(\mathstrut -\mathstrut 116866x^{28} \) \(\mathstrut +\mathstrut 313439x^{27} \) \(\mathstrut +\mathstrut 3761516x^{26} \) \(\mathstrut -\mathstrut 16528202x^{25} \) \(\mathstrut -\mathstrut 69577575x^{24} \) \(\mathstrut +\mathstrut 454590453x^{23} \) \(\mathstrut +\mathstrut 661153716x^{22} \) \(\mathstrut -\mathstrut 7733535779x^{21} \) \(\mathstrut -\mathstrut 175319215x^{20} \) \(\mathstrut +\mathstrut 85663905890x^{19} \) \(\mathstrut -\mathstrut 77230371437x^{18} \) \(\mathstrut -\mathstrut 620521532016x^{17} \) \(\mathstrut +\mathstrut 1015547163823x^{16} \) \(\mathstrut +\mathstrut 2826119182089x^{15} \) \(\mathstrut -\mathstrut 6857289879369x^{14} \) \(\mathstrut -\mathstrut 7065850709040x^{13} \) \(\mathstrut +\mathstrut 27261526134530x^{12} \) \(\mathstrut +\mathstrut 4123593429018x^{11} \) \(\mathstrut -\mathstrut 62635914256836x^{10} \) \(\mathstrut +\mathstrut 23660591791338x^{9} \) \(\mathstrut +\mathstrut 73472868519262x^{8} \) \(\mathstrut -\mathstrut 54443637858924x^{7} \) \(\mathstrut -\mathstrut 30646182875952x^{6} \) \(\mathstrut +\mathstrut 33343730036440x^{5} \) \(\mathstrut +\mathstrut 1404674931980x^{4} \) \(\mathstrut -\mathstrut 5319225952360x^{3} \) \(\mathstrut +\mathstrut 292439972480x^{2} \) \(\mathstrut +\mathstrut 247333072992x \) \(\mathstrut -\mathstrut 15579258048\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $...$
9 $[9, 3, -w^{3} + 8w + 8]$ $\phantom{-}e$
16 $[16, 2, 2]$ $...$
19 $[19, 19, w + 1]$ $...$
19 $[19, 19, -w^{2} + 6]$ $...$
19 $[19, 19, -w^{2} + 2w + 5]$ $...$
19 $[19, 19, -w + 2]$ $...$
25 $[25, 5, 2w^{2} - 2w - 13]$ $...$
29 $[29, 29, -w^{2} + 9]$ $...$
29 $[29, 29, -w^{2} + 2w + 6]$ $...$
29 $[29, 29, w^{2} - 7]$ $...$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $...$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-1$
41 $[41, 41, -w]$ $...$
41 $[41, 41, -w + 1]$ $...$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $...$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $...$
61 $[61, 61, 2w^{2} - 3w - 14]$ $...$
61 $[61, 61, 2w^{2} - w - 15]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
31 $[31,31,-2w^{2} + 3w + 11]$ $1$