Base field \(\Q(\sqrt{30}) \)
Generator \(w\), with minimal polynomial \(x^{2} - 30\); narrow class number \(4\) and class number \(2\).
Form
| Weight: | $[2, 2]$ |
| Level: | $[7, 7, w + 3]$ |
| Dimension: | $12$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $32$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{12} - 32x^{10} + 734x^{8} - 10480x^{6} + 102129x^{4} - 526704x^{2} + 1345600\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 2 | $[2, 2, w]$ | $\phantom{-}\frac{8582217}{3837611149840}e^{11} - \frac{13074129}{239850696865}e^{9} + \frac{2520775579}{1918805574920}e^{7} - \frac{811911630}{47970139373}e^{5} + \frac{53970969741}{295200857680}e^{3} - \frac{250645288221}{479701393730}e$ |
| 3 | $[3, 3, w]$ | $-\frac{80761471}{3837611149840}e^{11} + \frac{1099873081}{1918805574920}e^{9} - \frac{5851344463}{479701393730}e^{7} + \frac{58575589571}{383761114984}e^{5} - \frac{354238225173}{295200857680}e^{3} + \frac{1611157080053}{479701393730}e$ |
| 5 | $[5, 5, -w + 5]$ | $\phantom{-}\frac{8582217}{3837611149840}e^{11} - \frac{13074129}{239850696865}e^{9} + \frac{2520775579}{1918805574920}e^{7} - \frac{811911630}{47970139373}e^{5} + \frac{53970969741}{295200857680}e^{3} - \frac{730346681951}{479701393730}e$ |
| 7 | $[7, 7, w + 3]$ | $-\frac{1809}{103738496}e^{10} + \frac{6797}{12967312}e^{8} - \frac{575279}{51869248}e^{6} + \frac{476051}{3241828}e^{4} - \frac{118203041}{103738496}e^{2} + \frac{47377959}{12967312}$ |
| 7 | $[7, 7, w + 4]$ | $\phantom{-}\frac{588267}{26466283792}e^{10} - \frac{8159811}{13233141896}e^{8} + \frac{94635971}{6616570948}e^{6} - \frac{2380880153}{13233141896}e^{4} + \frac{3531008605}{2035867984}e^{2} - \frac{19526020031}{3308285474}$ |
| 13 | $[13, 13, w + 2]$ | $\phantom{-}\frac{588267}{13233141896}e^{10} - \frac{8159811}{6616570948}e^{8} + \frac{94635971}{3308285474}e^{6} - \frac{2380880153}{6616570948}e^{4} + \frac{3531008605}{1017933992}e^{2} - \frac{19526020031}{1654142737}$ |
| 13 | $[13, 13, w + 11]$ | $-\frac{495397}{13233141896}e^{10} + \frac{7765799}{6616570948}e^{8} - \frac{177171075}{6616570948}e^{6} + \frac{2322421325}{6616570948}e^{4} - \frac{3015984137}{1017933992}e^{2} + \frac{16090820899}{1654142737}$ |
| 17 | $[17, 17, w + 8]$ | $-\frac{11167961}{479701393730}e^{11} + \frac{1204466113}{1918805574920}e^{9} - \frac{25926153431}{1918805574920}e^{7} + \frac{65070882611}{383761114984}e^{5} - \frac{204104597457}{147600428840}e^{3} + \frac{930901184137}{239850696865}e$ |
| 17 | $[17, 17, w + 9]$ | $\phantom{-}\frac{7445957}{239850696865}e^{11} - \frac{1539538727}{1918805574920}e^{9} + \frac{31970202009}{1918805574920}e^{7} - \frac{80582119905}{383761114984}e^{5} + \frac{233167525663}{147600428840}e^{3} - \frac{1061984545223}{239850696865}e$ |
| 19 | $[19, 19, w + 7]$ | $-\frac{292073}{6616570948}e^{10} + \frac{3055915}{3308285474}e^{8} - \frac{117151049}{6616570948}e^{6} + \frac{211511112}{1654142737}e^{4} - \frac{58558480}{127241749}e^{2} - \frac{11660139870}{1654142737}$ |
| 19 | $[19, 19, -w + 7]$ | $\phantom{-}\frac{56418}{1654142737}e^{10} - \frac{1084307}{1654142737}e^{8} + \frac{21541986}{1654142737}e^{6} - \frac{150750546}{1654142737}e^{4} + \frac{39543776}{127241749}e^{2} + \frac{6586055650}{1654142737}$ |
| 29 | $[29, 29, -w - 1]$ | $\phantom{-}0$ |
| 29 | $[29, 29, w - 1]$ | $\phantom{-}\frac{387505}{383761114984}e^{11} - \frac{29114571}{383761114984}e^{9} + \frac{1171090649}{383761114984}e^{7} - \frac{22472607925}{383761114984}e^{5} + \frac{9901364287}{14760042884}e^{3} - \frac{256982949346}{47970139373}e$ |
| 37 | $[37, 37, w + 17]$ | $\phantom{-}\frac{1737691}{13233141896}e^{10} - \frac{48906945}{13233141896}e^{8} + \frac{1033275965}{13233141896}e^{6} - \frac{13398876615}{13233141896}e^{4} + \frac{1067935419}{127241749}e^{2} - \frac{45456595408}{1654142737}$ |
| 37 | $[37, 37, w + 20]$ | $\phantom{-}\frac{1737691}{13233141896}e^{10} - \frac{48906945}{13233141896}e^{8} + \frac{1033275965}{13233141896}e^{6} - \frac{13398876615}{13233141896}e^{4} + \frac{1067935419}{127241749}e^{2} - \frac{45456595408}{1654142737}$ |
| 71 | $[71, 71, 2w - 7]$ | $\phantom{-}\frac{1661173}{479701393730}e^{11} - \frac{63613209}{1918805574920}e^{9} - \frac{813902087}{1918805574920}e^{7} + \frac{9482021845}{383761114984}e^{5} - \frac{45042673129}{147600428840}e^{3} + \frac{554568064779}{239850696865}e$ |
| 71 | $[71, 71, -2w - 7]$ | $-\frac{10098963}{1918805574920}e^{11} - \frac{252118509}{1918805574920}e^{9} + \frac{4880998963}{1918805574920}e^{7} - \frac{31202621171}{383761114984}e^{5} + \frac{31579976049}{36900107210}e^{3} - \frac{1379193146996}{239850696865}e$ |
| 83 | $[83, 83, w + 14]$ | $\phantom{-}\frac{157477969}{3837611149840}e^{11} - \frac{544613161}{479701393730}e^{9} + \frac{48329033863}{1918805574920}e^{7} - \frac{15140727621}{47970139373}e^{5} + \frac{812263503157}{295200857680}e^{3} - \frac{3712083302597}{479701393730}e$ |
| 83 | $[83, 83, w + 69]$ | $-\frac{51001031}{3837611149840}e^{11} + \frac{141388049}{479701393730}e^{9} - \frac{9567321577}{1918805574920}e^{7} + \frac{6131795387}{95940278746}e^{5} - \frac{62280743083}{295200857680}e^{3} + \frac{273688156123}{479701393730}e$ |
| 101 | $[101, 101, -7w + 37]$ | $\phantom{-}\frac{1661173}{479701393730}e^{11} - \frac{63613209}{1918805574920}e^{9} - \frac{813902087}{1918805574920}e^{7} + \frac{9482021845}{383761114984}e^{5} - \frac{45042673129}{147600428840}e^{3} + \frac{554568064779}{239850696865}e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $7$ | $[7, 7, w + 3]$ | $\frac{1809}{103738496}e^{10} - \frac{6797}{12967312}e^{8} + \frac{575279}{51869248}e^{6} - \frac{476051}{3241828}e^{4} + \frac{118203041}{103738496}e^{2} - \frac{47377959}{12967312}$ |