Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 29
Level $[29,29,-w^{2} + 7]$
Label 4.4.17725.1-29.3-b
Dimension 30
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 $[29,29,-w^{2} + 7]$
Label 4.4.17725.1-29.3-b
Dimension 30
Is CM no
Is base change no
Parent newspace dimension 52

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{30} \) \(\mathstrut -\mathstrut x^{29} \) \(\mathstrut -\mathstrut 143x^{28} \) \(\mathstrut +\mathstrut 148x^{27} \) \(\mathstrut +\mathstrut 8832x^{26} \) \(\mathstrut -\mathstrut 9491x^{25} \) \(\mathstrut -\mathstrut 310365x^{24} \) \(\mathstrut +\mathstrut 349143x^{23} \) \(\mathstrut +\mathstrut 6882882x^{22} \) \(\mathstrut -\mathstrut 8185313x^{21} \) \(\mathstrut -\mathstrut 101055570x^{20} \) \(\mathstrut +\mathstrut 128220926x^{19} \) \(\mathstrut +\mathstrut 1003204381x^{18} \) \(\mathstrut -\mathstrut 1369219262x^{17} \) \(\mathstrut -\mathstrut 6760035880x^{16} \) \(\mathstrut +\mathstrut 10011860208x^{15} \) \(\mathstrut +\mathstrut 30576382323x^{14} \) \(\mathstrut -\mathstrut 49789358243x^{13} \) \(\mathstrut -\mathstrut 90012743698x^{12} \) \(\mathstrut +\mathstrut 165319819619x^{11} \) \(\mathstrut +\mathstrut 160889528180x^{10} \) \(\mathstrut -\mathstrut 353573619968x^{9} \) \(\mathstrut -\mathstrut 145029815736x^{8} \) \(\mathstrut +\mathstrut 455361857584x^{7} \) \(\mathstrut +\mathstrut 16214610784x^{6} \) \(\mathstrut -\mathstrut 309436127424x^{5} \) \(\mathstrut +\mathstrut 57995756160x^{4} \) \(\mathstrut +\mathstrut 83546149632x^{3} \) \(\mathstrut -\mathstrut 17935225856x^{2} \) \(\mathstrut -\mathstrut 7362103296x \) \(\mathstrut +\mathstrut 226039808\)

  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 $[29, 29, w^{2} - 7]$ $-1$
29 $[29, 29, -w^{2} + 2w + 8]$ $...$
31 $[31, 31, -2w^{2} + w + 12]$ $...$
31 $[31, 31, 2w^{2} - 3w - 11]$ $...$
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
29 $[29,29,-w^{2} + 7]$ $1$