Newspace parameters
| Level: | \( N \) | = | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Character orbit: | \([\chi]\) | = | 140.h (of order \(2\) and degree \(1\)) |
Newform invariants
| Self dual: | Yes |
| Analytic conductor: | \(0.0698691017686\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Projective image | \(D_{3}\) |
| Projective field | Galois closure of 3.1.140.1 |
| Artin image size | \(12\) |
| Artin image | $D_6$ |
| Artin field | Galois closure of 6.2.98000.1 |
$q$-expansion
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
| \(n\) | \(57\) | \(71\) | \(101\) |
| \(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 69.1 |
|
0 | 1.00000 | 0 | −1.00000 | 0 | −1.00000 | 0 | 0 | 0 | |||||||||||||||||||||
Inner twists
| Char. orbit | Parity | Mult. | Self Twist | Proved |
|---|---|---|---|---|
| 1.a | Even | 1 | trivial | yes |
| 35.c | Odd | 1 | CM by \(\Q(\sqrt{-35}) \) | yes |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{1}^{\mathrm{new}}(140, [\chi])\).