Newspace parameters
Level: | \( N \) | \(=\) | \( 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 211.d (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(1.68484348265\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.
Embeddings
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Label | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
55.1 | −0.823713 | − | 2.53513i | 1.09276 | + | 0.793934i | −4.13033 | + | 3.00086i | −2.20904 | + | 1.60496i | 1.11261 | − | 3.42425i | −1.40617 | + | 4.32774i | 6.69675 | + | 4.86547i | −0.363265 | − | 1.11802i | 5.88840 | + | 4.27817i |
55.2 | −0.783034 | − | 2.40993i | 0.126121 | + | 0.0916323i | −3.57660 | + | 2.59855i | 1.92447 | − | 1.39821i | 0.122071 | − | 0.375694i | 1.02238 | − | 3.14656i | 4.96291 | + | 3.60576i | −0.919541 | − | 2.83006i | −4.87651 | − | 3.54299i |
55.3 | −0.601014 | − | 1.84973i | 2.58570 | + | 1.87862i | −1.44225 | + | 1.04785i | 1.58388 | − | 1.15076i | 1.92090 | − | 5.91192i | −0.332824 | + | 1.02433i | −0.341891 | − | 0.248398i | 2.22958 | + | 6.86194i | −3.08052 | − | 2.23813i |
55.4 | −0.494908 | − | 1.52317i | 0.161827 | + | 0.117574i | −0.457083 | + | 0.332090i | −0.346918 | + | 0.252050i | 0.0989960 | − | 0.304678i | 0.262972 | − | 0.809344i | −1.85933 | − | 1.35088i | −0.914687 | − | 2.81512i | 0.555609 | + | 0.403673i |
55.5 | −0.369787 | − | 1.13809i | −1.30350 | − | 0.947050i | 0.459534 | − | 0.333871i | −2.74223 | + | 1.99234i | −0.595807 | + | 1.83371i | −0.492385 | + | 1.51540i | −2.48613 | − | 1.80628i | −0.124836 | − | 0.384205i | 3.28150 | + | 2.38415i |
55.6 | −0.306400 | − | 0.943001i | −2.37872 | − | 1.72824i | 0.822664 | − | 0.597700i | 1.68704 | − | 1.22570i | −0.900893 | + | 2.77266i | 0.670719 | − | 2.06426i | −2.42002 | − | 1.75825i | 1.74444 | + | 5.36882i | −1.67275 | − | 1.21532i |
55.7 | −0.174343 | − | 0.536572i | 0.321270 | + | 0.233417i | 1.36052 | − | 0.988476i | 3.24511 | − | 2.35771i | 0.0692335 | − | 0.213079i | −1.30076 | + | 4.00333i | −1.68045 | − | 1.22092i | −0.878320 | − | 2.70319i | −1.83084 | − | 1.33018i |
55.8 | 0.00729930 | + | 0.0224649i | 2.04906 | + | 1.48873i | 1.61758 | − | 1.17524i | −2.91308 | + | 2.11648i | −0.0184875 | + | 0.0568986i | −0.724895 | + | 2.23100i | 0.0764286 | + | 0.0555286i | 1.05528 | + | 3.24781i | −0.0688100 | − | 0.0499934i |
55.9 | 0.0769537 | + | 0.236839i | 1.22311 | + | 0.888642i | 1.56786 | − | 1.13912i | 0.142587 | − | 0.103595i | −0.116342 | + | 0.358065i | 0.992095 | − | 3.05335i | 0.793375 | + | 0.576421i | −0.220736 | − | 0.679355i | 0.0355080 | + | 0.0257981i |
55.10 | 0.157742 | + | 0.485481i | −1.10206 | − | 0.800692i | 1.40723 | − | 1.02241i | 0.529046 | − | 0.384375i | 0.214879 | − | 0.661331i | −0.670812 | + | 2.06455i | 1.54429 | + | 1.12199i | −0.353628 | − | 1.08835i | 0.270059 | + | 0.196210i |
55.11 | 0.207152 | + | 0.637549i | −1.13296 | − | 0.823147i | 1.25448 | − | 0.911431i | −2.19752 | + | 1.59659i | 0.290101 | − | 0.892838i | 1.58364 | − | 4.87395i | 1.92561 | + | 1.39904i | −0.321013 | − | 0.987977i | −1.47312 | − | 1.07029i |
55.12 | 0.429487 | + | 1.32183i | −2.68143 | − | 1.94817i | 0.0552709 | − | 0.0401567i | −1.41131 | + | 1.02537i | 1.42350 | − | 4.38110i | −0.906281 | + | 2.78925i | 2.32564 | + | 1.68968i | 2.46764 | + | 7.59460i | −1.96150 | − | 1.42512i |
55.13 | 0.600382 | + | 1.84779i | −1.20922 | − | 0.878551i | −1.43582 | + | 1.04318i | 3.00251 | − | 2.18145i | 0.897379 | − | 2.76185i | 0.713624 | − | 2.19631i | 0.354019 | + | 0.257210i | −0.236686 | − | 0.728445i | 5.83351 | + | 4.23829i |
55.14 | 0.723652 | + | 2.22717i | 1.60963 | + | 1.16946i | −2.81859 | + | 2.04783i | −1.52835 | + | 1.11041i | −1.43979 | + | 4.43120i | 0.795165 | − | 2.44727i | −2.81145 | − | 2.04264i | 0.296207 | + | 0.911631i | −3.57907 | − | 2.60034i |
55.15 | 0.850529 | + | 2.61766i | −1.17060 | − | 0.850488i | −4.51071 | + | 3.27722i | −0.384227 | + | 0.279157i | 1.23066 | − | 3.78759i | −0.970402 | + | 2.98659i | −7.96171 | − | 5.78452i | −0.280085 | − | 0.862012i | −1.05754 | − | 0.768345i |
71.1 | −2.00568 | + | 1.45721i | −0.880080 | − | 2.70861i | 1.28126 | − | 3.94330i | 1.09752 | − | 3.37781i | 5.71218 | + | 4.15014i | −2.94866 | − | 2.14233i | 1.64423 | + | 5.06042i | −4.13497 | + | 3.00423i | 2.72092 | + | 8.37413i |
71.2 | −1.84928 | + | 1.34358i | 0.783219 | + | 2.41050i | 0.996596 | − | 3.06721i | −0.917830 | + | 2.82479i | −4.68709 | − | 3.40537i | −1.47046 | − | 1.06835i | 0.865332 | + | 2.66322i | −2.77002 | + | 2.01254i | −2.09801 | − | 6.45701i |
71.3 | −1.84532 | + | 1.34070i | 0.186810 | + | 0.574942i | 0.989681 | − | 3.04592i | 0.379148 | − | 1.16690i | −1.11555 | − | 0.810494i | −0.287656 | − | 0.208994i | 0.847703 | + | 2.60896i | 2.13139 | − | 1.54855i | 0.864813 | + | 2.66162i |
71.4 | −1.36230 | + | 0.989770i | −0.936978 | − | 2.88372i | 0.258187 | − | 0.794617i | −0.871071 | + | 2.68088i | 4.13067 | + | 3.00111i | 1.63788 | + | 1.18999i | −0.605946 | − | 1.86491i | −5.01087 | + | 3.64061i | −1.46679 | − | 4.51433i |
71.5 | −1.15099 | + | 0.836242i | −0.102365 | − | 0.315048i | 0.00743956 | − | 0.0228966i | 0.347159 | − | 1.06844i | 0.381278 | + | 0.277015i | 2.21212 | + | 1.60720i | −0.868693 | − | 2.67356i | 2.33827 | − | 1.69886i | 0.493903 | + | 1.52008i |
See all 60 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
211.d | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 211.2.d.b | ✓ | 60 |
211.d | even | 5 | 1 | inner | 211.2.d.b | ✓ | 60 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
211.2.d.b | ✓ | 60 | 1.a | even | 1 | 1 | trivial |
211.2.d.b | ✓ | 60 | 211.d | even | 5 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{60} + 2 T_{2}^{59} + 21 T_{2}^{58} + 38 T_{2}^{57} + 280 T_{2}^{56} + 528 T_{2}^{55} + 3112 T_{2}^{54} + 6056 T_{2}^{53} + 30782 T_{2}^{52} + 60044 T_{2}^{51} + 251223 T_{2}^{50} + 478633 T_{2}^{49} + 1794064 T_{2}^{48} + \cdots + 361 \)
acting on \(S_{2}^{\mathrm{new}}(211, [\chi])\).