Newspace parameters
Level: | \( N \) | = | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | = | \( 1 \) |
Character orbit: | \([\chi]\) | = | 140.p (of order \(6\) and degree \(2\)) |
Newform invariants
Self dual: | No |
Analytic conductor: | \(0.0698691017686\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Projective image | \(D_{3}\) |
Projective field | Galois closure of 3.1.980.1 |
$q$-expansion
The \(q\)-expansion and trace form are shown below.
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-\zeta_{6}\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
39.1 |
|
0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | −0.500000 | − | 0.866025i | −1.00000 | 0.500000 | − | 0.866025i | −1.00000 | 0 | 0.500000 | − | 0.866025i | ||||||||||||
79.1 | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | −0.500000 | + | 0.866025i | −1.00000 | 0.500000 | + | 0.866025i | −1.00000 | 0 | 0.500000 | + | 0.866025i |
Inner twists
Char. orbit | Parity | Mult. | Self Twist | Proved |
---|---|---|---|---|
1.a | Even | 1 | trivial | yes |
20.d | Odd | 1 | CM by \(\Q(\sqrt{-5}) \) | yes |
7.c | Even | 1 | yes | |
140.p | Odd | 1 | yes |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{3}^{2} + T_{3} + 1 \) acting on \(S_{1}^{\mathrm{new}}(140, [\chi])\).