Newspace parameters
Level: | \( N \) | \(=\) | \( 805 = 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 805.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(6.42795736271\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Relative dimension: | \(13\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
116.1 | −1.21151 | − | 2.09840i | 0.545639 | − | 0.945074i | −1.93551 | + | 3.35240i | −0.500000 | − | 0.866025i | −2.64419 | −1.33047 | + | 2.28689i | 4.53352 | 0.904556 | + | 1.56674i | −1.21151 | + | 2.09840i | ||||
116.2 | −0.930075 | − | 1.61094i | −0.647848 | + | 1.12211i | −0.730080 | + | 1.26454i | −0.500000 | − | 0.866025i | 2.41019 | −0.321023 | − | 2.62620i | −1.00418 | 0.660585 | + | 1.14417i | −0.930075 | + | 1.61094i | ||||
116.3 | −0.808540 | − | 1.40043i | 0.950902 | − | 1.64701i | −0.307475 | + | 0.532562i | −0.500000 | − | 0.866025i | −3.07537 | −1.85596 | − | 1.88558i | −2.23974 | −0.308430 | − | 0.534217i | −0.808540 | + | 1.40043i | ||||
116.4 | −0.403896 | − | 0.699568i | −0.435726 | + | 0.754699i | 0.673736 | − | 1.16695i | −0.500000 | − | 0.866025i | 0.703952 | 2.64245 | + | 0.132096i | −2.70406 | 1.12029 | + | 1.94039i | −0.403896 | + | 0.699568i | ||||
116.5 | −0.315573 | − | 0.546589i | −0.746000 | + | 1.29211i | 0.800827 | − | 1.38707i | −0.500000 | − | 0.866025i | 0.941671 | −1.51243 | + | 2.17084i | −2.27317 | 0.386967 | + | 0.670247i | −0.315573 | + | 0.546589i | ||||
116.6 | 0.0122895 | + | 0.0212861i | 1.20990 | − | 2.09561i | 0.999698 | − | 1.73153i | −0.500000 | − | 0.866025i | 0.0594766 | −0.797907 | + | 2.52257i | 0.0983013 | −1.42773 | − | 2.47291i | 0.0122895 | − | 0.0212861i | ||||
116.7 | 0.331631 | + | 0.574401i | 0.0704605 | − | 0.122041i | 0.780042 | − | 1.35107i | −0.500000 | − | 0.866025i | 0.0934675 | 2.61178 | − | 0.422600i | 2.36127 | 1.49007 | + | 2.58088i | 0.331631 | − | 0.574401i | ||||
116.8 | 0.407561 | + | 0.705916i | 1.49351 | − | 2.58683i | 0.667789 | − | 1.15664i | −0.500000 | − | 0.866025i | 2.43478 | 2.16383 | + | 1.52245i | 2.71890 | −2.96114 | − | 5.12884i | 0.407561 | − | 0.705916i | ||||
116.9 | 0.715027 | + | 1.23846i | −0.647175 | + | 1.12094i | −0.0225278 | + | 0.0390193i | −0.500000 | − | 0.866025i | −1.85099 | −2.26678 | + | 1.36444i | 2.79568 | 0.662330 | + | 1.14719i | 0.715027 | − | 1.23846i | ||||
116.10 | 0.818862 | + | 1.41831i | −0.993060 | + | 1.72003i | −0.341070 | + | 0.590750i | −0.500000 | − | 0.866025i | −3.25272 | 0.0983737 | − | 2.64392i | 2.15829 | −0.472336 | − | 0.818110i | 0.818862 | − | 1.41831i | ||||
116.11 | 1.22768 | + | 2.12640i | 0.865673 | − | 1.49939i | −2.01438 | + | 3.48901i | −0.500000 | − | 0.866025i | 4.25107 | 0.636983 | − | 2.56793i | −4.98133 | 0.00121936 | + | 0.00211200i | 1.22768 | − | 2.12640i | ||||
116.12 | 1.26952 | + | 2.19888i | 0.797397 | − | 1.38113i | −2.22339 | + | 3.85102i | −0.500000 | − | 0.866025i | 4.04926 | −2.50585 | + | 0.848950i | −6.21247 | 0.228316 | + | 0.395455i | 1.26952 | − | 2.19888i | ||||
116.13 | 1.38702 | + | 2.40239i | −1.46368 | + | 2.53516i | −2.84766 | + | 4.93230i | −0.500000 | − | 0.866025i | −8.12060 | 2.43700 | + | 1.03006i | −10.2510 | −2.78469 | − | 4.82323i | 1.38702 | − | 2.40239i | ||||
576.1 | −1.21151 | + | 2.09840i | 0.545639 | + | 0.945074i | −1.93551 | − | 3.35240i | −0.500000 | + | 0.866025i | −2.64419 | −1.33047 | − | 2.28689i | 4.53352 | 0.904556 | − | 1.56674i | −1.21151 | − | 2.09840i | ||||
576.2 | −0.930075 | + | 1.61094i | −0.647848 | − | 1.12211i | −0.730080 | − | 1.26454i | −0.500000 | + | 0.866025i | 2.41019 | −0.321023 | + | 2.62620i | −1.00418 | 0.660585 | − | 1.14417i | −0.930075 | − | 1.61094i | ||||
576.3 | −0.808540 | + | 1.40043i | 0.950902 | + | 1.64701i | −0.307475 | − | 0.532562i | −0.500000 | + | 0.866025i | −3.07537 | −1.85596 | + | 1.88558i | −2.23974 | −0.308430 | + | 0.534217i | −0.808540 | − | 1.40043i | ||||
576.4 | −0.403896 | + | 0.699568i | −0.435726 | − | 0.754699i | 0.673736 | + | 1.16695i | −0.500000 | + | 0.866025i | 0.703952 | 2.64245 | − | 0.132096i | −2.70406 | 1.12029 | − | 1.94039i | −0.403896 | − | 0.699568i | ||||
576.5 | −0.315573 | + | 0.546589i | −0.746000 | − | 1.29211i | 0.800827 | + | 1.38707i | −0.500000 | + | 0.866025i | 0.941671 | −1.51243 | − | 2.17084i | −2.27317 | 0.386967 | − | 0.670247i | −0.315573 | − | 0.546589i | ||||
576.6 | 0.0122895 | − | 0.0212861i | 1.20990 | + | 2.09561i | 0.999698 | + | 1.73153i | −0.500000 | + | 0.866025i | 0.0594766 | −0.797907 | − | 2.52257i | 0.0983013 | −1.42773 | + | 2.47291i | 0.0122895 | + | 0.0212861i | ||||
576.7 | 0.331631 | − | 0.574401i | 0.0704605 | + | 0.122041i | 0.780042 | + | 1.35107i | −0.500000 | + | 0.866025i | 0.0934675 | 2.61178 | + | 0.422600i | 2.36127 | 1.49007 | − | 2.58088i | 0.331631 | + | 0.574401i | ||||
See all 26 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
7.c | even | 3 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 805.2.i.d | ✓ | 26 |
7.c | even | 3 | 1 | inner | 805.2.i.d | ✓ | 26 |
7.c | even | 3 | 1 | 5635.2.a.be | 13 | ||
7.d | odd | 6 | 1 | 5635.2.a.bf | 13 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
805.2.i.d | ✓ | 26 | 1.a | even | 1 | 1 | trivial |
805.2.i.d | ✓ | 26 | 7.c | even | 3 | 1 | inner |
5635.2.a.be | 13 | 7.c | even | 3 | 1 | ||
5635.2.a.bf | 13 | 7.d | odd | 6 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{26} - 5 T_{2}^{25} + 32 T_{2}^{24} - 95 T_{2}^{23} + 394 T_{2}^{22} - 942 T_{2}^{21} + 3126 T_{2}^{20} - 5999 T_{2}^{19} + 16174 T_{2}^{18} - 25410 T_{2}^{17} + 59664 T_{2}^{16} - 77081 T_{2}^{15} + 153225 T_{2}^{14} - 157790 T_{2}^{13} + \cdots + 4 \)
acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\).