Properties

Base field 4.4.17725.1
Weight [2, 2, 2, 2]
Level norm 19
Level $[19,19,-w + 2]$
Label 4.4.17725.1-19.4-f
Dimension 7
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 $[19,19,-w + 2]$
Label 4.4.17725.1-19.4-f
Dimension 7
Is CM no
Is base change no
Parent newspace dimension 32

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{7} \) \(\mathstrut +\mathstrut 7x^{6} \) \(\mathstrut -\mathstrut 4x^{5} \) \(\mathstrut -\mathstrut 97x^{4} \) \(\mathstrut -\mathstrut 72x^{3} \) \(\mathstrut +\mathstrut 332x^{2} \) \(\mathstrut +\mathstrut 336x \) \(\mathstrut -\mathstrut 64\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
9 $[9, 3, -w^{3} + 3w^{2} + 5w - 15]$ $\phantom{-}e$
9 $[9, 3, -w^{3} + 8w + 8]$ $-\frac{37}{1616}e^{6} - \frac{265}{1616}e^{5} - \frac{13}{808}e^{4} + \frac{3017}{1616}e^{3} + \frac{1795}{808}e^{2} - \frac{1157}{202}e - \frac{374}{101}$
16 $[16, 2, 2]$ $\phantom{-}\frac{29}{808}e^{6} + \frac{235}{808}e^{5} + \frac{1}{202}e^{4} - \frac{2725}{808}e^{3} - \frac{205}{101}e^{2} + \frac{1669}{202}e + \frac{185}{101}$
19 $[19, 19, w + 1]$ $-\frac{1}{16}e^{6} - \frac{5}{16}e^{5} + \frac{7}{8}e^{4} + \frac{69}{16}e^{3} - \frac{33}{8}e^{2} - \frac{25}{2}e + 6$
19 $[19, 19, -w^{2} + 6]$ $-\frac{11}{404}e^{6} - \frac{133}{808}e^{5} + \frac{293}{808}e^{4} + \frac{529}{202}e^{3} - \frac{849}{808}e^{2} - \frac{3497}{404}e - \frac{412}{101}$
19 $[19, 19, -w^{2} + 2w + 5]$ $\phantom{-}\frac{115}{3232}e^{6} + \frac{507}{3232}e^{5} - \frac{915}{1616}e^{4} - \frac{6975}{3232}e^{3} + \frac{3773}{1616}e^{2} + \frac{2799}{404}e + \frac{543}{101}$
19 $[19, 19, -w + 2]$ $-1$
25 $[25, 5, 2w^{2} - 2w - 13]$ $\phantom{-}\frac{29}{1616}e^{6} + \frac{33}{1616}e^{5} - \frac{503}{808}e^{4} - \frac{1513}{1616}e^{3} + \frac{2917}{808}e^{2} + \frac{493}{101}e + \frac{244}{101}$
29 $[29, 29, -w^{2} + 9]$ $-\frac{29}{404}e^{6} - \frac{67}{202}e^{5} + \frac{501}{404}e^{4} + \frac{2119}{404}e^{3} - \frac{2501}{404}e^{2} - \frac{3641}{202}e + \frac{438}{101}$
29 $[29, 29, -w^{2} + 2w + 6]$ $\phantom{-}\frac{77}{3232}e^{6} + \frac{617}{3232}e^{5} - \frac{235}{1616}e^{4} - \frac{10537}{3232}e^{3} - \frac{2327}{1616}e^{2} + \frac{1311}{101}e + \frac{714}{101}$
29 $[29, 29, w^{2} - 7]$ $\phantom{-}\frac{47}{1616}e^{6} + \frac{353}{1616}e^{5} - \frac{75}{404}e^{4} - \frac{4695}{1616}e^{3} + \frac{62}{101}e^{2} + \frac{3903}{404}e - \frac{120}{101}$
29 $[29, 29, -w^{2} + 2w + 8]$ $-\frac{47}{808}e^{6} - \frac{63}{202}e^{5} + \frac{401}{808}e^{4} + \frac{2877}{808}e^{3} + \frac{119}{808}e^{2} - \frac{2655}{404}e - \frac{366}{101}$
31 $[31, 31, -2w^{2} + w + 12]$ $\phantom{-}\frac{69}{808}e^{6} + \frac{385}{808}e^{5} - \frac{347}{404}e^{4} - \frac{4993}{808}e^{3} + \frac{769}{404}e^{2} + \frac{1740}{101}e + \frac{172}{101}$
31 $[31, 31, 2w^{2} - 3w - 11]$ $-\frac{63}{1616}e^{6} - \frac{413}{1616}e^{5} + \frac{16}{101}e^{4} + \frac{5279}{1616}e^{3} + \frac{1131}{404}e^{2} - \frac{3981}{404}e - \frac{847}{101}$
41 $[41, 41, -w]$ $-\frac{151}{1616}e^{6} - \frac{743}{1616}e^{5} + \frac{815}{808}e^{4} + \frac{8491}{1616}e^{3} - \frac{2365}{808}e^{2} - \frac{1254}{101}e - \frac{156}{101}$
41 $[41, 41, -w + 1]$ $\phantom{-}\frac{57}{3232}e^{6} + \frac{441}{3232}e^{5} + \frac{91}{1616}e^{4} - \frac{3949}{3232}e^{3} - \frac{3677}{1616}e^{2} + \frac{19}{404}e + \frac{1107}{101}$
49 $[49, 7, w^{3} + 2w^{2} - 10w - 20]$ $\phantom{-}\frac{297}{3232}e^{6} + \frac{1341}{3232}e^{5} - \frac{2811}{1616}e^{4} - \frac{22405}{3232}e^{3} + \frac{15553}{1616}e^{2} + \frac{5049}{202}e - \frac{781}{101}$
49 $[49, 7, w^{3} - 5w^{2} - 3w + 27]$ $-\frac{309}{3232}e^{6} - \frac{1285}{3232}e^{5} + \frac{2441}{1616}e^{4} + \frac{16985}{3232}e^{3} - \frac{13535}{1616}e^{2} - \frac{6567}{404}e + \frac{1037}{101}$
61 $[61, 61, 2w^{2} - 3w - 14]$ $-\frac{113}{3232}e^{6} - \frac{853}{3232}e^{5} + \frac{539}{1616}e^{4} + \frac{14477}{3232}e^{3} - \frac{305}{1616}e^{2} - \frac{4143}{202}e - \frac{653}{101}$
61 $[61, 61, 2w^{2} - w - 15]$ $-\frac{37}{1616}e^{6} - \frac{63}{1616}e^{5} + \frac{123}{202}e^{4} + \frac{1805}{1616}e^{3} - \frac{971}{404}e^{2} - \frac{2213}{404}e - \frac{71}{101}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
19 $[19,19,-w + 2]$ $1$