Newspace parameters
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.606863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 76) |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.76.1 |
Artin image: | $D_6$ |
Artin field: | Galois closure of 6.2.739328.3 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1025.1 |
|
0 | 0 | 0 | 1.00000 | 0 | −1.00000 | 0 | 1.00000 | 0 | |||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
19.b | odd | 2 | 1 | CM by \(\Q(\sqrt{-19}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 1216.1.e.a | 1 | |
4.b | odd | 2 | 1 | 1216.1.e.b | 1 | ||
8.b | even | 2 | 1 | 76.1.c.a | ✓ | 1 | |
8.d | odd | 2 | 1 | 304.1.e.a | 1 | ||
19.b | odd | 2 | 1 | CM | 1216.1.e.a | 1 | |
24.f | even | 2 | 1 | 2736.1.o.b | 1 | ||
24.h | odd | 2 | 1 | 684.1.h.a | 1 | ||
40.f | even | 2 | 1 | 1900.1.e.a | 1 | ||
40.i | odd | 4 | 2 | 1900.1.g.a | 2 | ||
56.h | odd | 2 | 1 | 3724.1.e.c | 1 | ||
56.j | odd | 6 | 2 | 3724.1.bc.b | 2 | ||
56.p | even | 6 | 2 | 3724.1.bc.c | 2 | ||
76.d | even | 2 | 1 | 1216.1.e.b | 1 | ||
152.b | even | 2 | 1 | 304.1.e.a | 1 | ||
152.g | odd | 2 | 1 | 76.1.c.a | ✓ | 1 | |
152.l | odd | 6 | 2 | 1444.1.h.a | 2 | ||
152.p | even | 6 | 2 | 1444.1.h.a | 2 | ||
152.s | odd | 18 | 6 | 1444.1.j.a | 6 | ||
152.t | even | 18 | 6 | 1444.1.j.a | 6 | ||
456.l | odd | 2 | 1 | 2736.1.o.b | 1 | ||
456.p | even | 2 | 1 | 684.1.h.a | 1 | ||
760.b | odd | 2 | 1 | 1900.1.e.a | 1 | ||
760.t | even | 4 | 2 | 1900.1.g.a | 2 | ||
1064.f | even | 2 | 1 | 3724.1.e.c | 1 | ||
1064.br | odd | 6 | 2 | 3724.1.bc.c | 2 | ||
1064.cf | even | 6 | 2 | 3724.1.bc.b | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
76.1.c.a | ✓ | 1 | 8.b | even | 2 | 1 | |
76.1.c.a | ✓ | 1 | 152.g | odd | 2 | 1 | |
304.1.e.a | 1 | 8.d | odd | 2 | 1 | ||
304.1.e.a | 1 | 152.b | even | 2 | 1 | ||
684.1.h.a | 1 | 24.h | odd | 2 | 1 | ||
684.1.h.a | 1 | 456.p | even | 2 | 1 | ||
1216.1.e.a | 1 | 1.a | even | 1 | 1 | trivial | |
1216.1.e.a | 1 | 19.b | odd | 2 | 1 | CM | |
1216.1.e.b | 1 | 4.b | odd | 2 | 1 | ||
1216.1.e.b | 1 | 76.d | even | 2 | 1 | ||
1444.1.h.a | 2 | 152.l | odd | 6 | 2 | ||
1444.1.h.a | 2 | 152.p | even | 6 | 2 | ||
1444.1.j.a | 6 | 152.s | odd | 18 | 6 | ||
1444.1.j.a | 6 | 152.t | even | 18 | 6 | ||
1900.1.e.a | 1 | 40.f | even | 2 | 1 | ||
1900.1.e.a | 1 | 760.b | odd | 2 | 1 | ||
1900.1.g.a | 2 | 40.i | odd | 4 | 2 | ||
1900.1.g.a | 2 | 760.t | even | 4 | 2 | ||
2736.1.o.b | 1 | 24.f | even | 2 | 1 | ||
2736.1.o.b | 1 | 456.l | odd | 2 | 1 | ||
3724.1.e.c | 1 | 56.h | odd | 2 | 1 | ||
3724.1.e.c | 1 | 1064.f | even | 2 | 1 | ||
3724.1.bc.b | 2 | 56.j | odd | 6 | 2 | ||
3724.1.bc.b | 2 | 1064.cf | even | 6 | 2 | ||
3724.1.bc.c | 2 | 56.p | even | 6 | 2 | ||
3724.1.bc.c | 2 | 1064.br | odd | 6 | 2 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7} + 1 \)
acting on \(S_{1}^{\mathrm{new}}(1216, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T \)
$5$
\( T - 1 \)
$7$
\( T + 1 \)
$11$
\( T - 1 \)
$13$
\( T \)
$17$
\( T + 1 \)
$19$
\( T + 1 \)
$23$
\( T - 2 \)
$29$
\( T \)
$31$
\( T \)
$37$
\( T \)
$41$
\( T \)
$43$
\( T - 1 \)
$47$
\( T + 1 \)
$53$
\( T \)
$59$
\( T \)
$61$
\( T - 1 \)
$67$
\( T \)
$71$
\( T \)
$73$
\( T + 1 \)
$79$
\( T \)
$83$
\( T + 2 \)
$89$
\( T \)
$97$
\( T \)
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