Newspace parameters
Level: | \( N \) | = | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Character orbit: | \([\chi]\) | = | 1800.l (of order \(2\) and degree \(1\)) |
Newform invariants
Self dual: | No |
Analytic conductor: | \(0.898317022739\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Projective image | \(S_{4}\) |
Projective field | Galois closure of 4.2.10800.2 |
Artin image size | \(48\) |
Artin image | $\GL(2,3)$ |
Artin field | Galois closure of 8.2.1399680000.1 |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{-2}\). We also show the integral \(q\)-expansion of the trace form.
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1601.1 |
|
0 | 0 | 0 | 0 | 0 | −1.00000 | 0 | 0 | 0 | ||||||||||||||||||||||||
1601.2 | 0 | 0 | 0 | 0 | 0 | −1.00000 | 0 | 0 | 0 |
Inner twists
Char. orbit | Parity | Mult. | Self Twist | Proved |
---|---|---|---|---|
1.a | Even | 1 | trivial | yes |
3.b | Odd | 1 | yes |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{7} + 1 \) acting on \(S_{1}^{\mathrm{new}}(1800, [\chi])\).