Properties

Base field \(\Q(\sqrt{114}) \)
Weight [2, 2]
Level norm 3
Level $[3, 3, w]$
Label 2.2.456.1-3.1-g
Dimension 40
CM no
Base change no

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Base field \(\Q(\sqrt{114}) \)

Generator \(w\), with minimal polynomial \(x^{2} - 114\); narrow class number \(4\) and class number \(2\).

Form

Weight [2, 2]
Level $[3, 3, w]$
Label 2.2.456.1-3.1-g
Dimension 40
Is CM no
Is base change no
Parent newspace dimension 72

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{40} \) \(\mathstrut +\mathstrut 78x^{38} \) \(\mathstrut +\mathstrut 3427x^{36} \) \(\mathstrut +\mathstrut 100518x^{34} \) \(\mathstrut +\mathstrut 2149623x^{32} \) \(\mathstrut +\mathstrut 34362036x^{30} \) \(\mathstrut +\mathstrut 412862574x^{28} \) \(\mathstrut +\mathstrut 3525284148x^{26} \) \(\mathstrut +\mathstrut 18365243355x^{24} \) \(\mathstrut +\mathstrut 9577738782x^{22} \) \(\mathstrut -\mathstrut 675871851669x^{20} \) \(\mathstrut -\mathstrut 4954475195322x^{18} \) \(\mathstrut -\mathstrut 2337027044091x^{16} \) \(\mathstrut +\mathstrut 55875232531008x^{14} \) \(\mathstrut +\mathstrut 155863366914924x^{12} \) \(\mathstrut +\mathstrut 140520666010944x^{10} \) \(\mathstrut +\mathstrut 964807914758160x^{8} \) \(\mathstrut +\mathstrut 1156924017002496x^{6} \) \(\mathstrut +\mathstrut 1358164965738496x^{4} \) \(\mathstrut -\mathstrut 631283393888256x^{2} \) \(\mathstrut +\mathstrut 2812739227549696\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
2 $[2, 2, -3w - 32]$ $...$
3 $[3, 3, w]$ $...$
5 $[5, 5, w + 2]$ $...$
5 $[5, 5, w + 3]$ $...$
7 $[7, 7, -w + 11]$ $...$
7 $[7, 7, w + 11]$ $...$
11 $[11, 11, w + 2]$ $...$
11 $[11, 11, w + 9]$ $...$
13 $[13, 13, w + 6]$ $...$
13 $[13, 13, w + 7]$ $...$
19 $[19, 19, w]$ $...$
37 $[37, 37, w + 15]$ $...$
37 $[37, 37, w + 22]$ $...$
41 $[41, 41, 37w + 395]$ $...$
41 $[41, 41, 5w + 53]$ $...$
67 $[67, 67, w + 28]$ $...$
67 $[67, 67, w + 39]$ $...$
71 $[71, 71, 40w + 427]$ $...$
71 $[71, 71, 8w + 85]$ $...$
73 $[73, 73, -2w + 23]$ $...$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
3 $[3, 3, w]$ $\frac{504208324302619012876582078355493011915256260593483089764160839356789}{4126403868917208953702928066518430724102522567130595378247023869747781761656296783872}e^{38} + \frac{20638673205384701623227009493656902960872684723036506814723546802340159}{2063201934458604476851464033259215362051261283565297689123511934873890880828148391936}e^{36} + \frac{268274332186618656738515865474249909140612170549238467433740819604893953}{589486266988172707671846866645490103443217509590085054035289124249683108808042397696}e^{34} + \frac{28601819109120354374198446756520909839295988120417818942604299801416381167}{2063201934458604476851464033259215362051261283565297689123511934873890880828148391936}e^{32} + \frac{1272868129409251224112707058568334449548522806380211041575217962254221986131}{4126403868917208953702928066518430724102522567130595378247023869747781761656296783872}e^{30} + \frac{5328488450154612770661707442880882499739962599923146990056567986040961897223}{1031600967229302238425732016629607681025630641782648844561755967436945440414074195968}e^{28} + \frac{135434429203309309989703133714288402750677266733149282090467903799869444609631}{2063201934458604476851464033259215362051261283565297689123511934873890880828148391936}e^{26} + \frac{628660402681260559914918432250055352860059802244323075242275879474469294478199}{1031600967229302238425732016629607681025630641782648844561755967436945440414074195968}e^{24} + \frac{15334070184838362687628433681069246738639570233913991143477391354572843379256335}{4126403868917208953702928066518430724102522567130595378247023869747781761656296783872}e^{22} + \frac{17024843450058163640775062478750589483440509677657682237628743518087380531758067}{2063201934458604476851464033259215362051261283565297689123511934873890880828148391936}e^{20} - \frac{353260924032162332211038038689396474690590632645896954834739382399853200518838425}{4126403868917208953702928066518430724102522567130595378247023869747781761656296783872}e^{18} - \frac{1895060865915031483747437324937029989313374464413102521142641779103898532301461149}{2063201934458604476851464033259215362051261283565297689123511934873890880828148391936}e^{16} - \frac{1326936669624628507594851325409886168088299210970307162011584907906096721054079177}{589486266988172707671846866645490103443217509590085054035289124249683108808042397696}e^{14} + \frac{520128024353824547642451611324368001107917519856824577500639941777183200775716389}{64475060451831389901608251039350480064101915111415552785109747964809090025879637248}e^{12} + \frac{45745676881380713857733961270568585376559719938271000860069005627473168741668334703}{1031600967229302238425732016629607681025630641782648844561755967436945440414074195968}e^{10} + \frac{3438120458406357651408873257391281815515027180271115694059011745999573404537232121}{64475060451831389901608251039350480064101915111415552785109747964809090025879637248}e^{8} + \frac{33485121565117306590967694772176832395655708590655026601834152246078960678237970141}{257900241807325559606433004157401920256407660445662211140438991859236360103518548992}e^{6} + \frac{5189987037712072869706190468506784765782156280460335748476901346062408293849750415}{8059382556478923737701031379918810008012739388926944098138718495601136253234954656}e^{4} + \frac{1941342686044641085109240347599548190755737190459428690384227000521681480286638071}{4029691278239461868850515689959405004006369694463472049069359247800568126617477328}e^{2} + \frac{44490234820740283961329369213788081565035693353895835250102375677977653961839262}{251855704889966366803157230622462812750398105903967003066834952987535507913592333}$