Newspace parameters
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.u (of order \(4\), degree \(2\), not minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 720) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
$q$-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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
719.1 | 0 | 0 | 0 | −2.23581 | + | 0.0342493i | 0 | 4.97879i | 0 | 0 | 0 | ||||||||||||||||
719.2 | 0 | 0 | 0 | −2.22047 | + | 0.263678i | 0 | − | 2.95946i | 0 | 0 | 0 | |||||||||||||||
719.3 | 0 | 0 | 0 | −2.21921 | − | 0.274088i | 0 | 1.32258i | 0 | 0 | 0 | ||||||||||||||||
719.4 | 0 | 0 | 0 | −2.19631 | − | 0.419806i | 0 | 0.263783i | 0 | 0 | 0 | ||||||||||||||||
719.5 | 0 | 0 | 0 | −2.18619 | − | 0.469629i | 0 | − | 2.94937i | 0 | 0 | 0 | |||||||||||||||
719.6 | 0 | 0 | 0 | −2.14049 | + | 0.646750i | 0 | − | 0.594230i | 0 | 0 | 0 | |||||||||||||||
719.7 | 0 | 0 | 0 | −1.93984 | − | 1.11222i | 0 | 1.78786i | 0 | 0 | 0 | ||||||||||||||||
719.8 | 0 | 0 | 0 | −1.91479 | − | 1.15480i | 0 | 3.02955i | 0 | 0 | 0 | ||||||||||||||||
719.9 | 0 | 0 | 0 | −1.81012 | + | 1.31281i | 0 | 1.40695i | 0 | 0 | 0 | ||||||||||||||||
719.10 | 0 | 0 | 0 | −1.73123 | − | 1.41522i | 0 | 3.80565i | 0 | 0 | 0 | ||||||||||||||||
719.11 | 0 | 0 | 0 | −1.71042 | + | 1.44030i | 0 | − | 2.04714i | 0 | 0 | 0 | |||||||||||||||
719.12 | 0 | 0 | 0 | −1.65197 | + | 1.50698i | 0 | 4.30751i | 0 | 0 | 0 | ||||||||||||||||
719.13 | 0 | 0 | 0 | −1.50698 | + | 1.65197i | 0 | − | 4.30751i | 0 | 0 | 0 | |||||||||||||||
719.14 | 0 | 0 | 0 | −1.44030 | + | 1.71042i | 0 | 2.04714i | 0 | 0 | 0 | ||||||||||||||||
719.15 | 0 | 0 | 0 | −1.41522 | − | 1.73123i | 0 | − | 3.80565i | 0 | 0 | 0 | |||||||||||||||
719.16 | 0 | 0 | 0 | −1.31281 | + | 1.81012i | 0 | − | 1.40695i | 0 | 0 | 0 | |||||||||||||||
719.17 | 0 | 0 | 0 | −1.15480 | − | 1.91479i | 0 | − | 3.02955i | 0 | 0 | 0 | |||||||||||||||
719.18 | 0 | 0 | 0 | −1.11222 | − | 1.93984i | 0 | − | 1.78786i | 0 | 0 | 0 | |||||||||||||||
719.19 | 0 | 0 | 0 | −0.646750 | + | 2.14049i | 0 | 0.594230i | 0 | 0 | 0 | ||||||||||||||||
719.20 | 0 | 0 | 0 | −0.469629 | − | 2.18619i | 0 | 2.94937i | 0 | 0 | 0 | ||||||||||||||||
See all 96 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
3.b | odd | 2 | 1 | inner |
5.b | even | 2 | 1 | inner |
15.d | odd | 2 | 1 | inner |
16.f | odd | 4 | 1 | inner |
48.k | even | 4 | 1 | inner |
80.k | odd | 4 | 1 | inner |
240.t | even | 4 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2880.2.u.a | 96 | |
3.b | odd | 2 | 1 | inner | 2880.2.u.a | 96 | |
4.b | odd | 2 | 1 | 720.2.u.a | ✓ | 96 | |
5.b | even | 2 | 1 | inner | 2880.2.u.a | 96 | |
12.b | even | 2 | 1 | 720.2.u.a | ✓ | 96 | |
15.d | odd | 2 | 1 | inner | 2880.2.u.a | 96 | |
16.e | even | 4 | 1 | 720.2.u.a | ✓ | 96 | |
16.f | odd | 4 | 1 | inner | 2880.2.u.a | 96 | |
20.d | odd | 2 | 1 | 720.2.u.a | ✓ | 96 | |
48.i | odd | 4 | 1 | 720.2.u.a | ✓ | 96 | |
48.k | even | 4 | 1 | inner | 2880.2.u.a | 96 | |
60.h | even | 2 | 1 | 720.2.u.a | ✓ | 96 | |
80.k | odd | 4 | 1 | inner | 2880.2.u.a | 96 | |
80.q | even | 4 | 1 | 720.2.u.a | ✓ | 96 | |
240.t | even | 4 | 1 | inner | 2880.2.u.a | 96 | |
240.bm | odd | 4 | 1 | 720.2.u.a | ✓ | 96 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
720.2.u.a | ✓ | 96 | 4.b | odd | 2 | 1 | |
720.2.u.a | ✓ | 96 | 12.b | even | 2 | 1 | |
720.2.u.a | ✓ | 96 | 16.e | even | 4 | 1 | |
720.2.u.a | ✓ | 96 | 20.d | odd | 2 | 1 | |
720.2.u.a | ✓ | 96 | 48.i | odd | 4 | 1 | |
720.2.u.a | ✓ | 96 | 60.h | even | 2 | 1 | |
720.2.u.a | ✓ | 96 | 80.q | even | 4 | 1 | |
720.2.u.a | ✓ | 96 | 240.bm | odd | 4 | 1 | |
2880.2.u.a | 96 | 1.a | even | 1 | 1 | trivial | |
2880.2.u.a | 96 | 3.b | odd | 2 | 1 | inner | |
2880.2.u.a | 96 | 5.b | even | 2 | 1 | inner | |
2880.2.u.a | 96 | 15.d | odd | 2 | 1 | inner | |
2880.2.u.a | 96 | 16.f | odd | 4 | 1 | inner | |
2880.2.u.a | 96 | 48.k | even | 4 | 1 | inner | |
2880.2.u.a | 96 | 80.k | odd | 4 | 1 | inner | |
2880.2.u.a | 96 | 240.t | even | 4 | 1 | inner |
Hecke kernels
This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(2880, [\chi])\).