Properties

Label 3.3.1929.1-7.3-b
Base field 3.3.1929.1
Weight $[2, 2, 2]$
Level norm $7$
Level $[7, 7, -w^{2} + 9]$
Dimension $11$
CM no
Base change no

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Base field 3.3.1929.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 10x + 13\); narrow class number \(2\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[7, 7, -w^{2} + 9]$
Dimension: $11$
CM: no
Base change: no
Newspace dimension: $22$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{11} - 19x^{9} + 115x^{7} - 8x^{6} - 241x^{5} + 70x^{4} + 133x^{3} - 38x^{2} - 15x - 1\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w - 2]$ $\phantom{-}e$
3 $[3, 3, w - 1]$ $-\frac{3947}{1783}e^{10} - \frac{1727}{1783}e^{9} + \frac{73403}{1783}e^{8} + \frac{31727}{1783}e^{7} - \frac{424827}{1783}e^{6} - \frac{146603}{1783}e^{5} + \frac{802220}{1783}e^{4} + \frac{33695}{1783}e^{3} - \frac{360205}{1783}e^{2} + \frac{28130}{1783}e + \frac{6190}{1783}$
7 $[7, 7, w^{2} + w - 7]$ $\phantom{-}\frac{479}{1783}e^{10} - \frac{1947}{1783}e^{9} - \frac{10303}{1783}e^{8} + \frac{36098}{1783}e^{7} + \frac{76908}{1783}e^{6} - \frac{210887}{1783}e^{5} - \frac{220966}{1783}e^{4} + \frac{414189}{1783}e^{3} + \frac{138042}{1783}e^{2} - \frac{180191}{1783}e - \frac{22458}{1783}$
7 $[7, 7, -w^{2} + 11]$ $\phantom{-}\frac{4195}{1783}e^{10} + \frac{544}{1783}e^{9} - \frac{78849}{1783}e^{8} - \frac{9933}{1783}e^{7} + \frac{467136}{1783}e^{6} + \frac{20596}{1783}e^{5} - \frac{932753}{1783}e^{4} + \frac{210409}{1783}e^{3} + \frac{458871}{1783}e^{2} - \frac{139629}{1783}e - \frac{25962}{1783}$
7 $[7, 7, -w^{2} + 9]$ $-1$
8 $[8, 2, 2]$ $\phantom{-}\frac{1422}{1783}e^{10} - \frac{1276}{1783}e^{9} - \frac{27977}{1783}e^{8} + \frac{24282}{1783}e^{7} + \frac{180290}{1783}e^{6} - \frac{156391}{1783}e^{5} - \frac{420373}{1783}e^{4} + \frac{385709}{1783}e^{3} + \frac{239938}{1783}e^{2} - \frac{189099}{1783}e - \frac{27441}{1783}$
13 $[13, 13, -w]$ $\phantom{-}\frac{215}{1783}e^{10} - \frac{55}{1783}e^{9} - \frac{3988}{1783}e^{8} + \frac{647}{1783}e^{7} + \frac{23357}{1783}e^{6} - \frac{1807}{1783}e^{5} - \frac{46294}{1783}e^{4} + \frac{1516}{1783}e^{3} + \frac{18919}{1783}e^{2} + \frac{9879}{1783}e - \frac{30}{1783}$
19 $[19, 19, -w^{2} - w + 4]$ $-\frac{1456}{1783}e^{10} + \frac{2114}{1783}e^{9} + \frac{29155}{1783}e^{8} - \frac{39262}{1783}e^{7} - \frac{193927}{1783}e^{6} + \frac{236862}{1783}e^{5} + \frac{475611}{1783}e^{4} - \frac{512351}{1783}e^{3} - \frac{274717}{1783}e^{2} + \frac{221223}{1783}e + \frac{33085}{1783}$
23 $[23, 23, w^{2} + w - 10]$ $\phantom{-}\frac{3292}{1783}e^{10} + \frac{2558}{1783}e^{9} - \frac{60673}{1783}e^{8} - \frac{46884}{1783}e^{7} + \frac{343718}{1783}e^{6} + \frac{237153}{1783}e^{5} - \frac{614578}{1783}e^{4} - \frac{235646}{1783}e^{3} + \frac{259237}{1783}e^{2} + \frac{73135}{1783}e + \frac{909}{1783}$
29 $[29, 29, 2w^{2} - 21]$ $\phantom{-}\frac{2380}{1783}e^{10} + \frac{5528}{1783}e^{9} - \frac{41451}{1783}e^{8} - \frac{101435}{1783}e^{7} + \frac{203947}{1783}e^{6} + \frac{552257}{1783}e^{5} - \frac{222208}{1783}e^{4} - \frac{847061}{1783}e^{3} + \frac{4301}{1783}e^{2} + \frac{333104}{1783}e + \frac{36406}{1783}$
37 $[37, 37, 2w^{2} + w - 17]$ $\phantom{-}\frac{690}{1783}e^{10} + \frac{2187}{1783}e^{9} - \frac{11845}{1783}e^{8} - \frac{40218}{1783}e^{7} + \frac{55554}{1783}e^{6} + \frac{222176}{1783}e^{5} - \frac{44494}{1783}e^{4} - \frac{359696}{1783}e^{3} - \frac{17984}{1783}e^{2} + \frac{132382}{1783}e + \frac{20968}{1783}$
43 $[43, 43, 3w^{2} + 3w - 22]$ $-\frac{12724}{1783}e^{10} - \frac{2716}{1783}e^{9} + \frac{238636}{1783}e^{8} + \frac{49002}{1783}e^{7} - \frac{1406134}{1783}e^{6} - \frac{163503}{1783}e^{5} + \frac{2768172}{1783}e^{4} - \frac{469017}{1783}e^{3} - \frac{1323769}{1783}e^{2} + \frac{334894}{1783}e + \frac{67083}{1783}$
47 $[47, 47, w^{2} - 6]$ $-\frac{4175}{1783}e^{10} - \frac{3659}{1783}e^{9} + \frac{77317}{1783}e^{8} + \frac{66676}{1783}e^{7} - \frac{441494}{1783}e^{6} - \frac{338843}{1783}e^{5} + \frac{803139}{1783}e^{4} + \frac{360914}{1783}e^{3} - \frac{357968}{1783}e^{2} - \frac{106128}{1783}e - \frac{5886}{1783}$
47 $[47, 47, w^{2} - 3]$ $-\frac{8274}{1783}e^{10} - \frac{3108}{1783}e^{9} + \frac{154518}{1783}e^{8} + \frac{56920}{1783}e^{7} - \frac{901800}{1783}e^{6} - \frac{251657}{1783}e^{5} + \frac{1736725}{1783}e^{4} - \frac{34474}{1783}e^{3} - \frac{815341}{1783}e^{2} + \frac{116588}{1783}e + \frac{30885}{1783}$
47 $[47, 47, -w^{2} + 12]$ $\phantom{-}\frac{1236}{1783}e^{10} + \frac{5406}{1783}e^{9} - \frac{19435}{1783}e^{8} - \frac{99935}{1783}e^{7} + \frac{68769}{1783}e^{6} + \frac{559044}{1783}e^{5} + \frac{63992}{1783}e^{4} - \frac{938489}{1783}e^{3} - \frac{150544}{1783}e^{2} + \frac{378164}{1783}e + \frac{55142}{1783}$
53 $[53, 53, w^{2} - w - 4]$ $-\frac{7260}{1783}e^{10} + \frac{323}{1783}e^{9} + \frac{137111}{1783}e^{8} - \frac{5842}{1783}e^{7} - \frac{820966}{1783}e^{6} + \frac{92241}{1783}e^{5} + \frac{1679664}{1783}e^{4} - \frac{581862}{1783}e^{3} - \frac{853677}{1783}e^{2} + \frac{312977}{1783}e + \frac{58691}{1783}$
61 $[61, 61, w^{2} - 5]$ $\phantom{-}\frac{9144}{1783}e^{10} - \frac{1344}{1783}e^{9} - \frac{173019}{1783}e^{8} + \frac{24855}{1783}e^{7} + \frac{1040143}{1783}e^{6} - \frac{218696}{1783}e^{5} - \frac{2143612}{1783}e^{4} + \frac{933311}{1783}e^{3} + \frac{1079651}{1783}e^{2} - \frac{489688}{1783}e - \frac{84372}{1783}$
67 $[67, 67, w^{2} - w - 7]$ $\phantom{-}\frac{8037}{1783}e^{10} + \frac{5698}{1783}e^{9} - \frac{147775}{1783}e^{8} - \frac{105542}{1783}e^{7} + \frac{834903}{1783}e^{6} + \frac{537743}{1783}e^{5} - \frac{1486877}{1783}e^{4} - \frac{523999}{1783}e^{3} + \frac{607155}{1783}e^{2} + \frac{152959}{1783}e + \frac{3108}{1783}$
73 $[73, 73, 7w^{2} + 3w - 66]$ $\phantom{-}\frac{4595}{1783}e^{10} + \frac{5998}{1783}e^{9} - \frac{82744}{1783}e^{8} - \frac{110692}{1783}e^{7} + \frac{445076}{1783}e^{6} + \frac{591526}{1783}e^{5} - \frac{690063}{1783}e^{4} - \frac{804905}{1783}e^{3} + \frac{225002}{1783}e^{2} + \frac{301363}{1783}e + \frac{21750}{1783}$
79 $[79, 79, 2w^{2} - 19]$ $-\frac{3062}{1783}e^{10} - \frac{1829}{1783}e^{9} + \frac{55536}{1783}e^{8} + \frac{33478}{1783}e^{7} - \frac{305587}{1783}e^{6} - \frac{160717}{1783}e^{5} + \frac{507625}{1783}e^{4} + \frac{91974}{1783}e^{3} - \frac{157063}{1783}e^{2} - \frac{1074}{1783}e - \frac{8778}{1783}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$7$ $[7, 7, -w^{2} + 9]$ $1$