Newspace parameters
Level: | \( N \) | \(=\) | \( 140 = 2^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 140.h (of order \(2\), degree \(1\), minimal) |
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: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.140.1 |
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 | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
35.c | odd | 2 | 1 | CM by \(\Q(\sqrt{-35}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 140.1.h.b | yes | 1 |
3.b | odd | 2 | 1 | 1260.1.p.b | 1 | ||
4.b | odd | 2 | 1 | 560.1.p.a | 1 | ||
5.b | even | 2 | 1 | 140.1.h.a | ✓ | 1 | |
5.c | odd | 4 | 2 | 700.1.d.a | 2 | ||
7.b | odd | 2 | 1 | 140.1.h.a | ✓ | 1 | |
7.c | even | 3 | 2 | 980.1.n.a | 2 | ||
7.d | odd | 6 | 2 | 980.1.n.b | 2 | ||
8.b | even | 2 | 1 | 2240.1.p.b | 1 | ||
8.d | odd | 2 | 1 | 2240.1.p.d | 1 | ||
15.d | odd | 2 | 1 | 1260.1.p.a | 1 | ||
20.d | odd | 2 | 1 | 560.1.p.b | 1 | ||
20.e | even | 4 | 2 | 2800.1.f.c | 2 | ||
21.c | even | 2 | 1 | 1260.1.p.a | 1 | ||
28.d | even | 2 | 1 | 560.1.p.b | 1 | ||
28.f | even | 6 | 2 | 3920.1.br.a | 2 | ||
28.g | odd | 6 | 2 | 3920.1.br.b | 2 | ||
35.c | odd | 2 | 1 | CM | 140.1.h.b | yes | 1 |
35.f | even | 4 | 2 | 700.1.d.a | 2 | ||
35.i | odd | 6 | 2 | 980.1.n.a | 2 | ||
35.j | even | 6 | 2 | 980.1.n.b | 2 | ||
40.e | odd | 2 | 1 | 2240.1.p.a | 1 | ||
40.f | even | 2 | 1 | 2240.1.p.c | 1 | ||
56.e | even | 2 | 1 | 2240.1.p.a | 1 | ||
56.h | odd | 2 | 1 | 2240.1.p.c | 1 | ||
105.g | even | 2 | 1 | 1260.1.p.b | 1 | ||
140.c | even | 2 | 1 | 560.1.p.a | 1 | ||
140.j | odd | 4 | 2 | 2800.1.f.c | 2 | ||
140.p | odd | 6 | 2 | 3920.1.br.a | 2 | ||
140.s | even | 6 | 2 | 3920.1.br.b | 2 | ||
280.c | odd | 2 | 1 | 2240.1.p.b | 1 | ||
280.n | even | 2 | 1 | 2240.1.p.d | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
140.1.h.a | ✓ | 1 | 5.b | even | 2 | 1 | |
140.1.h.a | ✓ | 1 | 7.b | odd | 2 | 1 | |
140.1.h.b | yes | 1 | 1.a | even | 1 | 1 | trivial |
140.1.h.b | yes | 1 | 35.c | odd | 2 | 1 | CM |
560.1.p.a | 1 | 4.b | odd | 2 | 1 | ||
560.1.p.a | 1 | 140.c | even | 2 | 1 | ||
560.1.p.b | 1 | 20.d | odd | 2 | 1 | ||
560.1.p.b | 1 | 28.d | even | 2 | 1 | ||
700.1.d.a | 2 | 5.c | odd | 4 | 2 | ||
700.1.d.a | 2 | 35.f | even | 4 | 2 | ||
980.1.n.a | 2 | 7.c | even | 3 | 2 | ||
980.1.n.a | 2 | 35.i | odd | 6 | 2 | ||
980.1.n.b | 2 | 7.d | odd | 6 | 2 | ||
980.1.n.b | 2 | 35.j | even | 6 | 2 | ||
1260.1.p.a | 1 | 15.d | odd | 2 | 1 | ||
1260.1.p.a | 1 | 21.c | even | 2 | 1 | ||
1260.1.p.b | 1 | 3.b | odd | 2 | 1 | ||
1260.1.p.b | 1 | 105.g | even | 2 | 1 | ||
2240.1.p.a | 1 | 40.e | odd | 2 | 1 | ||
2240.1.p.a | 1 | 56.e | even | 2 | 1 | ||
2240.1.p.b | 1 | 8.b | even | 2 | 1 | ||
2240.1.p.b | 1 | 280.c | odd | 2 | 1 | ||
2240.1.p.c | 1 | 40.f | even | 2 | 1 | ||
2240.1.p.c | 1 | 56.h | odd | 2 | 1 | ||
2240.1.p.d | 1 | 8.d | odd | 2 | 1 | ||
2240.1.p.d | 1 | 280.n | even | 2 | 1 | ||
2800.1.f.c | 2 | 20.e | even | 4 | 2 | ||
2800.1.f.c | 2 | 140.j | odd | 4 | 2 | ||
3920.1.br.a | 2 | 28.f | even | 6 | 2 | ||
3920.1.br.a | 2 | 140.p | odd | 6 | 2 | ||
3920.1.br.b | 2 | 28.g | odd | 6 | 2 | ||
3920.1.br.b | 2 | 140.s | even | 6 | 2 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} - 1 \)
acting on \(S_{1}^{\mathrm{new}}(140, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 1 \)
$5$
\( T + 1 \)
$7$
\( T + 1 \)
$11$
\( T + 1 \)
$13$
\( T - 1 \)
$17$
\( T - 1 \)
$19$
\( T \)
$23$
\( T \)
$29$
\( T + 1 \)
$31$
\( T \)
$37$
\( T \)
$41$
\( T \)
$43$
\( T \)
$47$
\( T - 1 \)
$53$
\( T \)
$59$
\( T \)
$61$
\( T \)
$67$
\( T \)
$71$
\( T - 2 \)
$73$
\( T + 2 \)
$79$
\( T + 1 \)
$83$
\( T + 2 \)
$89$
\( T \)
$97$
\( T - 1 \)
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