Newspace parameters
Level: | \( N \) | \(=\) | \( 799 = 17 \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 799.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(6.38004712150\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
424.1 | −2.73159 | − | 2.93228i | 5.46157 | − | 0.487885i | 8.00977i | 0.803779i | −9.45559 | −5.59824 | 1.33270i | ||||||||||||||||
424.2 | −2.73159 | 2.93228i | 5.46157 | 0.487885i | − | 8.00977i | − | 0.803779i | −9.45559 | −5.59824 | − | 1.33270i | |||||||||||||||
424.3 | −2.67224 | − | 1.20994i | 5.14087 | 1.97515i | 3.23326i | 5.12847i | −8.39315 | 1.53604 | − | 5.27807i | ||||||||||||||||
424.4 | −2.67224 | 1.20994i | 5.14087 | − | 1.97515i | − | 3.23326i | − | 5.12847i | −8.39315 | 1.53604 | 5.27807i | |||||||||||||||
424.5 | −2.60183 | − | 0.179412i | 4.76951 | 3.93490i | 0.466798i | − | 2.38196i | −7.20579 | 2.96781 | − | 10.2379i | |||||||||||||||
424.6 | −2.60183 | 0.179412i | 4.76951 | − | 3.93490i | − | 0.466798i | 2.38196i | −7.20579 | 2.96781 | 10.2379i | ||||||||||||||||
424.7 | −2.12048 | − | 2.93288i | 2.49642 | − | 4.40553i | 6.21910i | − | 0.798156i | −1.05264 | −5.60179 | 9.34181i | |||||||||||||||
424.8 | −2.12048 | 2.93288i | 2.49642 | 4.40553i | − | 6.21910i | 0.798156i | −1.05264 | −5.60179 | − | 9.34181i | ||||||||||||||||
424.9 | −1.85975 | − | 0.458272i | 1.45866 | − | 2.56209i | 0.852271i | 0.0216061i | 1.00675 | 2.78999 | 4.76485i | ||||||||||||||||
424.10 | −1.85975 | 0.458272i | 1.45866 | 2.56209i | − | 0.852271i | − | 0.0216061i | 1.00675 | 2.78999 | − | 4.76485i | |||||||||||||||
424.11 | −1.50908 | − | 1.00039i | 0.277334 | 3.40854i | 1.50967i | 4.30933i | 2.59965 | 1.99922 | − | 5.14378i | ||||||||||||||||
424.12 | −1.50908 | 1.00039i | 0.277334 | − | 3.40854i | − | 1.50967i | − | 4.30933i | 2.59965 | 1.99922 | 5.14378i | |||||||||||||||
424.13 | −1.19759 | − | 2.00820i | −0.565770 | 1.69879i | 2.40500i | − | 3.98040i | 3.07275 | −1.03285 | − | 2.03446i | |||||||||||||||
424.14 | −1.19759 | 2.00820i | −0.565770 | − | 1.69879i | − | 2.40500i | 3.98040i | 3.07275 | −1.03285 | 2.03446i | ||||||||||||||||
424.15 | −1.13957 | − | 2.92459i | −0.701377 | − | 0.283746i | 3.33278i | − | 3.87426i | 3.07841 | −5.55325 | 0.323349i | |||||||||||||||
424.16 | −1.13957 | 2.92459i | −0.701377 | 0.283746i | − | 3.33278i | 3.87426i | 3.07841 | −5.55325 | − | 0.323349i | ||||||||||||||||
424.17 | −0.850575 | − | 3.02328i | −1.27652 | − | 0.477702i | 2.57153i | 3.15138i | 2.78693 | −6.14023 | 0.406322i | ||||||||||||||||
424.18 | −0.850575 | 3.02328i | −1.27652 | 0.477702i | − | 2.57153i | − | 3.15138i | 2.78693 | −6.14023 | − | 0.406322i | |||||||||||||||
424.19 | −0.262611 | − | 0.974571i | −1.93104 | 1.23574i | 0.255933i | − | 1.43778i | 1.03233 | 2.05021 | − | 0.324520i | |||||||||||||||
424.20 | −0.262611 | 0.974571i | −1.93104 | − | 1.23574i | − | 0.255933i | 1.43778i | 1.03233 | 2.05021 | 0.324520i | ||||||||||||||||
See all 40 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
17.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 799.2.b.c | ✓ | 40 |
17.b | even | 2 | 1 | inner | 799.2.b.c | ✓ | 40 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
799.2.b.c | ✓ | 40 | 1.a | even | 1 | 1 | trivial |
799.2.b.c | ✓ | 40 | 17.b | even | 2 | 1 | inner |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{20} + 3 T_{2}^{19} - 27 T_{2}^{18} - 83 T_{2}^{17} + 297 T_{2}^{16} + 950 T_{2}^{15} - 1701 T_{2}^{14} - 5829 T_{2}^{13} + 5329 T_{2}^{12} + 20800 T_{2}^{11} - 8418 T_{2}^{10} - 43846 T_{2}^{9} + 3462 T_{2}^{8} + 52825 T_{2}^{7} + \cdots + 17 \)
acting on \(S_{2}^{\mathrm{new}}(799, [\chi])\).