Newspace parameters
Level: | \( N \) | \(=\) | \( 639 = 3^{2} \cdot 71 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 639.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(5.10244068916\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 213) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
199.1 | −0.782687 | + | 2.40886i | 0 | −3.57199 | − | 2.59520i | −1.75584 | + | 1.27569i | 0 | −1.09908 | + | 3.38262i | 4.94904 | − | 3.59569i | 0 | −1.69869 | − | 5.22804i | ||||||
199.2 | −0.561101 | + | 1.72689i | 0 | −1.04928 | − | 0.762350i | −0.100283 | + | 0.0728600i | 0 | 0.566896 | − | 1.74473i | −1.03271 | + | 0.750310i | 0 | −0.0695523 | − | 0.214060i | ||||||
199.3 | −0.221575 | + | 0.681938i | 0 | 1.20209 | + | 0.873370i | 1.12207 | − | 0.815232i | 0 | 0.879183 | − | 2.70585i | −2.02212 | + | 1.46916i | 0 | 0.307315 | + | 0.945817i | ||||||
199.4 | 0.0386980 | − | 0.119100i | 0 | 1.60535 | + | 1.16635i | −1.70590 | + | 1.23941i | 0 | −0.521916 | + | 1.60629i | 0.403662 | − | 0.293278i | 0 | 0.0815989 | + | 0.251135i | ||||||
199.5 | 0.472579 | − | 1.45445i | 0 | −0.274058 | − | 0.199115i | 2.89570 | − | 2.10385i | 0 | −0.0936882 | + | 0.288343i | 2.05534 | − | 1.49329i | 0 | −1.69149 | − | 5.20588i | ||||||
199.6 | 0.863103 | − | 2.65636i | 0 | −4.69326 | − | 3.40985i | 0.0442495 | − | 0.0321491i | 0 | 1.50467 | − | 4.63091i | −8.58928 | + | 6.24048i | 0 | −0.0472077 | − | 0.145290i | ||||||
289.1 | −0.782687 | − | 2.40886i | 0 | −3.57199 | + | 2.59520i | −1.75584 | − | 1.27569i | 0 | −1.09908 | − | 3.38262i | 4.94904 | + | 3.59569i | 0 | −1.69869 | + | 5.22804i | ||||||
289.2 | −0.561101 | − | 1.72689i | 0 | −1.04928 | + | 0.762350i | −0.100283 | − | 0.0728600i | 0 | 0.566896 | + | 1.74473i | −1.03271 | − | 0.750310i | 0 | −0.0695523 | + | 0.214060i | ||||||
289.3 | −0.221575 | − | 0.681938i | 0 | 1.20209 | − | 0.873370i | 1.12207 | + | 0.815232i | 0 | 0.879183 | + | 2.70585i | −2.02212 | − | 1.46916i | 0 | 0.307315 | − | 0.945817i | ||||||
289.4 | 0.0386980 | + | 0.119100i | 0 | 1.60535 | − | 1.16635i | −1.70590 | − | 1.23941i | 0 | −0.521916 | − | 1.60629i | 0.403662 | + | 0.293278i | 0 | 0.0815989 | − | 0.251135i | ||||||
289.5 | 0.472579 | + | 1.45445i | 0 | −0.274058 | + | 0.199115i | 2.89570 | + | 2.10385i | 0 | −0.0936882 | − | 0.288343i | 2.05534 | + | 1.49329i | 0 | −1.69149 | + | 5.20588i | ||||||
289.6 | 0.863103 | + | 2.65636i | 0 | −4.69326 | + | 3.40985i | 0.0442495 | + | 0.0321491i | 0 | 1.50467 | + | 4.63091i | −8.58928 | − | 6.24048i | 0 | −0.0472077 | + | 0.145290i | ||||||
451.1 | −1.95351 | + | 1.41931i | 0 | 1.18374 | − | 3.64316i | 1.01092 | + | 3.11131i | 0 | −1.65679 | + | 1.20373i | 1.36598 | + | 4.20407i | 0 | −6.39076 | − | 4.64316i | ||||||
451.2 | −1.86334 | + | 1.35380i | 0 | 1.02125 | − | 3.14307i | −0.582378 | − | 1.79238i | 0 | 3.38602 | − | 2.46009i | 0.928686 | + | 2.85820i | 0 | 3.51169 | + | 2.55139i | ||||||
451.3 | −1.11950 | + | 0.813364i | 0 | −0.0263155 | + | 0.0809908i | −0.789118 | − | 2.42866i | 0 | −2.24566 | + | 1.63157i | −0.891637 | − | 2.74418i | 0 | 2.85880 | + | 2.07704i | ||||||
451.4 | 0.145962 | − | 0.106048i | 0 | −0.607975 | + | 1.87116i | 0.911171 | + | 2.80430i | 0 | −2.68661 | + | 1.95194i | 0.221196 | + | 0.680770i | 0 | 0.430386 | + | 0.312694i | ||||||
451.5 | 1.43997 | − | 1.04620i | 0 | 0.360951 | − | 1.11089i | 0.492126 | + | 1.51461i | 0 | 2.18360 | − | 1.58648i | 0.457583 | + | 1.40830i | 0 | 2.29323 | + | 1.66613i | ||||||
451.6 | 2.04140 | − | 1.48317i | 0 | 1.34951 | − | 4.15337i | −0.542726 | − | 1.67034i | 0 | −2.21662 | + | 1.61047i | −1.84574 | − | 5.68062i | 0 | −3.58531 | − | 2.60488i | ||||||
622.1 | −1.95351 | − | 1.41931i | 0 | 1.18374 | + | 3.64316i | 1.01092 | − | 3.11131i | 0 | −1.65679 | − | 1.20373i | 1.36598 | − | 4.20407i | 0 | −6.39076 | + | 4.64316i | ||||||
622.2 | −1.86334 | − | 1.35380i | 0 | 1.02125 | + | 3.14307i | −0.582378 | + | 1.79238i | 0 | 3.38602 | + | 2.46009i | 0.928686 | − | 2.85820i | 0 | 3.51169 | − | 2.55139i | ||||||
See all 24 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
71.c | even | 5 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 639.2.f.d | 24 | |
3.b | odd | 2 | 1 | 213.2.e.c | ✓ | 24 | |
71.c | even | 5 | 1 | inner | 639.2.f.d | 24 | |
213.h | odd | 10 | 1 | 213.2.e.c | ✓ | 24 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
213.2.e.c | ✓ | 24 | 3.b | odd | 2 | 1 | |
213.2.e.c | ✓ | 24 | 213.h | odd | 10 | 1 | |
639.2.f.d | 24 | 1.a | even | 1 | 1 | trivial | |
639.2.f.d | 24 | 71.c | even | 5 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{24} + 3 T_{2}^{23} + 14 T_{2}^{22} + 33 T_{2}^{21} + 120 T_{2}^{20} + 232 T_{2}^{19} + 771 T_{2}^{18} + 1527 T_{2}^{17} + 5570 T_{2}^{16} + 11089 T_{2}^{15} + 24491 T_{2}^{14} + 30579 T_{2}^{13} + 69694 T_{2}^{12} + 93123 T_{2}^{11} + \cdots + 121 \)
acting on \(S_{2}^{\mathrm{new}}(639, [\chi])\).