Properties

Base field \(\Q(\sqrt{5}, \sqrt{7})\)
Weight [2, 2, 2, 2]
Level norm 9
Level $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$
Label 4.4.19600.1-9.1-c
Dimension 8
CM no
Base change no

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Base field \(\Q(\sqrt{5}, \sqrt{7})\)

Generator \(w\), with minimal polynomial \(x^{4} - 2x^{3} - 15x^{2} + 16x + 29\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$
Label 4.4.19600.1-9.1-c
Dimension 8
Is CM no
Is base change no
Parent newspace dimension 18

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} \) \(\mathstrut -\mathstrut 149x^{6} \) \(\mathstrut +\mathstrut 7288x^{4} \) \(\mathstrut -\mathstrut 119797x^{2} \) \(\mathstrut +\mathstrut 105644\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
4 $[4, 2, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{1}{23}]$ $\phantom{-}\frac{2597}{1674161}e^{6} - \frac{275874}{1674161}e^{4} + \frac{7110480}{1674161}e^{2} - \frac{2404723}{1674161}$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w + \frac{24}{23}]$ $-1$
9 $[9, 3, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{68}{23}]$ $\phantom{-}\frac{4840}{1674161}e^{6} - \frac{512854}{1674161}e^{4} + \frac{13285889}{1674161}e^{2} - \frac{9962486}{1674161}$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w + \frac{24}{23}]$ $\phantom{-}e$
19 $[19, 19, -\frac{6}{23}w^{3} + \frac{9}{23}w^{2} + \frac{83}{23}w - \frac{20}{23}]$ $-\frac{39706}{82033889}e^{7} + \frac{4371959}{82033889}e^{5} - \frac{123883356}{82033889}e^{3} + \frac{403045207}{82033889}e$
19 $[19, 19, \frac{6}{23}w^{3} - \frac{9}{23}w^{2} - \frac{83}{23}w + \frac{66}{23}]$ $\phantom{-}e$
19 $[19, 19, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} - \frac{3}{23}w - \frac{22}{23}]$ $-\frac{39706}{82033889}e^{7} + \frac{4371959}{82033889}e^{5} - \frac{123883356}{82033889}e^{3} + \frac{403045207}{82033889}e$
25 $[25, 5, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{40}{23}w - \frac{21}{23}]$ $-\frac{116}{1674161}e^{6} + \frac{31662}{1674161}e^{4} - \frac{1479266}{1674161}e^{2} + \frac{4951326}{1674161}$
29 $[29, 29, w]$ $\phantom{-}\frac{2481}{1674161}e^{6} - \frac{244212}{1674161}e^{4} + \frac{5631214}{1674161}e^{2} + \frac{872442}{1674161}$
29 $[29, 29, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w - \frac{21}{23}]$ $\phantom{-}\frac{2481}{1674161}e^{6} - \frac{244212}{1674161}e^{4} + \frac{5631214}{1674161}e^{2} + \frac{872442}{1674161}$
29 $[29, 29, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{44}{23}]$ $\phantom{-}\frac{1120}{1674161}e^{6} - \frac{132513}{1674161}e^{4} + \frac{3544846}{1674161}e^{2} + \frac{7960974}{1674161}$
29 $[29, 29, -w + 1]$ $\phantom{-}\frac{1120}{1674161}e^{6} - \frac{132513}{1674161}e^{4} + \frac{3544846}{1674161}e^{2} + \frac{7960974}{1674161}$
31 $[31, 31, w + 2]$ $\phantom{-}\frac{5557}{82033889}e^{7} - \frac{506504}{82033889}e^{5} + \frac{10739021}{82033889}e^{3} - \frac{38286480}{82033889}e$
31 $[31, 31, -\frac{4}{23}w^{3} + \frac{6}{23}w^{2} + \frac{63}{23}w + \frac{25}{23}]$ $\phantom{-}\frac{5557}{82033889}e^{7} - \frac{506504}{82033889}e^{5} + \frac{10739021}{82033889}e^{3} - \frac{38286480}{82033889}e$
31 $[31, 31, \frac{4}{23}w^{3} - \frac{6}{23}w^{2} - \frac{63}{23}w + \frac{90}{23}]$ $-\frac{47841}{82033889}e^{7} + \frac{4773908}{82033889}e^{5} - \frac{100646808}{82033889}e^{3} - \frac{606225098}{82033889}e$
31 $[31, 31, -w + 3]$ $-\frac{47841}{82033889}e^{7} + \frac{4773908}{82033889}e^{5} - \frac{100646808}{82033889}e^{3} - \frac{606225098}{82033889}e$
49 $[49, 7, -\frac{2}{23}w^{3} + \frac{3}{23}w^{2} + \frac{43}{23}w - \frac{22}{23}]$ $\phantom{-}\frac{1535}{1674161}e^{6} - \frac{159192}{1674161}e^{4} + \frac{4305267}{1674161}e^{2} - \frac{2796394}{1674161}$
59 $[59, 59, -\frac{20}{23}w^{3} + \frac{30}{23}w^{2} + \frac{269}{23}w - \frac{128}{23}]$ $\phantom{-}\frac{36184}{82033889}e^{7} - \frac{3814743}{82033889}e^{5} + \frac{100676143}{82033889}e^{3} - \frac{186958589}{82033889}e$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{88}{23}]$ $\phantom{-}\frac{36184}{82033889}e^{7} - \frac{3814743}{82033889}e^{5} + \frac{100676143}{82033889}e^{3} - \frac{186958589}{82033889}e$
59 $[59, 59, -\frac{8}{23}w^{3} + \frac{12}{23}w^{2} + \frac{103}{23}w - \frac{19}{23}]$ $\phantom{-}\frac{73855}{82033889}e^{7} - \frac{8237414}{82033889}e^{5} + \frac{237027691}{82033889}e^{3} - \frac{849837823}{82033889}e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9,3,-\frac{2}{23}w^{3}+\frac{3}{23}w^{2}+\frac{43}{23}w+\frac{24}{23}]$ $1$