Properties

Base field 4.4.18688.1
Weight [2, 2, 2, 2]
Level norm 9
Level $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$
Label 4.4.18688.1-9.1-c
Dimension 16
CM no
Base change no

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Base field 4.4.18688.1

Generator \(w\), with minimal polynomial \(x^{4} - 10x^{2} - 4x + 14\); narrow class number \(2\) and class number \(1\).

Form

Weight [2, 2, 2, 2]
Level $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$
Label 4.4.18688.1-9.1-c
Dimension 16
Is CM no
Is base change no
Parent newspace dimension 22

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{16} \) \(\mathstrut -\mathstrut 21x^{14} \) \(\mathstrut +\mathstrut 174x^{12} \) \(\mathstrut -\mathstrut 724x^{10} \) \(\mathstrut +\mathstrut 1587x^{8} \) \(\mathstrut -\mathstrut 1747x^{6} \) \(\mathstrut +\mathstrut 822x^{4} \) \(\mathstrut -\mathstrut 120x^{2} \) \(\mathstrut +\mathstrut 4\)

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Norm Prime Eigenvalue
2 $[2, 2, -w - 2]$ $\phantom{-}e$
7 $[7, 7, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{7}{3}]$ $-\frac{1}{2}e^{15} + \frac{21}{2}e^{13} - 87e^{11} + \frac{723}{2}e^{9} - \frac{1573}{2}e^{7} + 841e^{5} - 354e^{3} + 30e$
7 $[7, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + w - \frac{5}{3}]$ $\phantom{-}\frac{1}{4}e^{15} - 5e^{13} + 39e^{11} - 150e^{9} + \frac{1171}{4}e^{7} - 260e^{5} + 67e^{3} + 5e$
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $-1$
9 $[9, 3, w + 1]$ $-\frac{1}{4}e^{14} + 5e^{12} - 39e^{10} + \frac{301}{2}e^{8} - \frac{1199}{4}e^{6} + \frac{583}{2}e^{4} - 115e^{2} + 9$
17 $[17, 17, w + 3]$ $\phantom{-}\frac{1}{4}e^{14} - 5e^{12} + \frac{79}{2}e^{10} - \frac{315}{2}e^{8} + \frac{1325}{4}e^{6} - \frac{679}{2}e^{4} + 127e^{2} - 7$
17 $[17, 17, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{11}{3}]$ $-\frac{1}{4}e^{14} + \frac{9}{2}e^{12} - \frac{63}{2}e^{10} + 112e^{8} - \frac{885}{4}e^{6} + \frac{479}{2}e^{4} - 115e^{2} + 9$
31 $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - w - \frac{1}{3}]$ $\phantom{-}\frac{1}{2}e^{13} - \frac{17}{2}e^{11} + \frac{107}{2}e^{9} - \frac{311}{2}e^{7} + 210e^{5} - 112e^{3} + 14e$
31 $[31, 31, -\frac{2}{3}w^{3} + \frac{2}{3}w^{2} + 5w - \frac{1}{3}]$ $-\frac{3}{2}e^{15} + 31e^{13} - 252e^{11} + \frac{2049}{2}e^{9} - \frac{4357}{2}e^{7} + \frac{4575}{2}e^{5} - 969e^{3} + 90e$
41 $[41, 41, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 4w - \frac{19}{3}]$ $\phantom{-}\frac{1}{2}e^{12} - \frac{17}{2}e^{10} + \frac{105}{2}e^{8} - \frac{285}{2}e^{6} + 158e^{4} - 46e^{2} + 4$
41 $[41, 41, w^{2} - 5]$ $-\frac{1}{2}e^{12} + 8e^{10} - \frac{91}{2}e^{8} + 110e^{6} - 100e^{4} + 10e^{2} + 6$
41 $[41, 41, 2w + 3]$ $\phantom{-}\frac{1}{4}e^{14} - 5e^{12} + 39e^{10} - \frac{301}{2}e^{8} + \frac{1195}{4}e^{6} - \frac{565}{2}e^{4} + 97e^{2} - 5$
41 $[41, 41, \frac{2}{3}w^{3} + \frac{4}{3}w^{2} - 5w - \frac{29}{3}]$ $\phantom{-}\frac{1}{2}e^{14} - \frac{19}{2}e^{12} + \frac{141}{2}e^{10} - \frac{523}{2}e^{8} + 508e^{6} - 478e^{4} + 162e^{2} - 8$
47 $[47, 47, -\frac{2}{3}w^{3} + \frac{5}{3}w^{2} + 3w - \frac{19}{3}]$ $-e^{13} + 17e^{11} - \frac{213}{2}e^{9} + 304e^{7} - \frac{777}{2}e^{5} + 175e^{3} - 12e$
47 $[47, 47, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - 3w - \frac{13}{3}]$ $-\frac{1}{4}e^{15} + 6e^{13} - \frac{113}{2}e^{11} + 265e^{9} - \frac{2597}{4}e^{7} + 791e^{5} - 399e^{3} + 49e$
49 $[49, 7, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 2w - \frac{11}{3}]$ $\phantom{-}\frac{1}{2}e^{14} - 10e^{12} + 78e^{10} - 301e^{8} + \frac{1197}{2}e^{6} - 574e^{4} + 212e^{2} - 16$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 5w + \frac{19}{3}]$ $-\frac{1}{4}e^{14} + \frac{13}{2}e^{12} - \frac{127}{2}e^{10} + 296e^{8} - \frac{2753}{4}e^{6} + \frac{1507}{2}e^{4} - 313e^{2} + 23$
73 $[73, 73, -\frac{2}{3}w^{3} - \frac{1}{3}w^{2} + 4w + \frac{11}{3}]$ $\phantom{-}\frac{1}{2}e^{14} - \frac{21}{2}e^{12} + 86e^{10} - \frac{693}{2}e^{8} + \frac{1417}{2}e^{6} - 674e^{4} + 222e^{2} - 8$
73 $[73, 73, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + 2w - \frac{17}{3}]$ $\phantom{-}e^{6} - 11e^{4} + 32e^{2} - 12$
103 $[103, 103, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + w - \frac{23}{3}]$ $\phantom{-}\frac{1}{2}e^{15} - \frac{21}{2}e^{13} + 86e^{11} - 347e^{9} + \frac{1431}{2}e^{7} - \frac{1411}{2}e^{5} + 275e^{3} - 42e$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + 3w - \frac{5}{3}]$ $1$