Newspace parameters
Level: | \( N \) | = | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | = | \( 1 \) |
Character orbit: | \([\chi]\) | = | 1800.c (of order \(2\) and degree \(1\)) |
Newform invariants
Self dual: | No |
Analytic conductor: | \(0.898317022739\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Projective image | \(S_{4}\) |
Projective field | Galois closure of 4.2.10800.2 |
$q$-expansion
The \(q\)-expansion and trace form are shown below.
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
449.1 |
|
0 | 0 | 0 | 0 | 0 | − | 1.00000i | 0 | 0 | 0 | |||||||||||||||||||||||||||||
449.2 | 0 | 0 | 0 | 0 | 0 | − | 1.00000i | 0 | 0 | 0 | ||||||||||||||||||||||||||||||
449.3 | 0 | 0 | 0 | 0 | 0 | 1.00000i | 0 | 0 | 0 | |||||||||||||||||||||||||||||||
449.4 | 0 | 0 | 0 | 0 | 0 | 1.00000i | 0 | 0 | 0 |
Inner twists
Char. orbit | Parity | Mult. | Self Twist | Proved |
---|---|---|---|---|
1.a | Even | 1 | trivial | yes |
3.b | Odd | 1 | yes | |
5.b | Even | 1 | yes | |
15.d | Odd | 1 | yes |
Hecke kernels
There are no other newforms in \(S_{1}^{\mathrm{new}}(1800, [\chi])\).