Newspace parameters
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1471.1 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | 3.34851 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.2 | 0 | 1.00000i | 0 | 1.00000i | 0 | 3.34851 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.3 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | −1.52302 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.4 | 0 | 1.00000i | 0 | 1.00000i | 0 | −1.52302 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.5 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | 3.12483 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.6 | 0 | 1.00000i | 0 | 1.00000i | 0 | 3.12483 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.7 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | 3.67125 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.8 | 0 | 1.00000i | 0 | 1.00000i | 0 | 3.67125 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.9 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | −1.53388 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.10 | 0 | 1.00000i | 0 | 1.00000i | 0 | −1.53388 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.11 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | −2.13359 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.12 | 0 | 1.00000i | 0 | 1.00000i | 0 | −2.13359 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.13 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | −3.74981 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.14 | 0 | 1.00000i | 0 | 1.00000i | 0 | −3.74981 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.15 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | 3.60511 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.16 | 0 | 1.00000i | 0 | 1.00000i | 0 | 3.60511 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.17 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | −0.143131 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.18 | 0 | 1.00000i | 0 | 1.00000i | 0 | −0.143131 | 0 | −1.00000 | 0 | ||||||||||||||||||
1471.19 | 0 | − | 1.00000i | 0 | − | 1.00000i | 0 | −2.01693 | 0 | −1.00000 | 0 | ||||||||||||||||
1471.20 | 0 | 1.00000i | 0 | 1.00000i | 0 | −2.01693 | 0 | −1.00000 | 0 | ||||||||||||||||||
See all 32 embeddings |
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
92.b | even | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 5520.2.be.c | ✓ | 32 |
4.b | odd | 2 | 1 | 5520.2.be.d | yes | 32 | |
23.b | odd | 2 | 1 | 5520.2.be.d | yes | 32 | |
92.b | even | 2 | 1 | inner | 5520.2.be.c | ✓ | 32 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
5520.2.be.c | ✓ | 32 | 1.a | even | 1 | 1 | trivial |
5520.2.be.c | ✓ | 32 | 92.b | even | 2 | 1 | inner |
5520.2.be.d | yes | 32 | 4.b | odd | 2 | 1 | |
5520.2.be.d | yes | 32 | 23.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \(T_{7}^{16} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(5520, [\chi])\).