Newspace parameters
Level: | \( N \) | \(=\) | \( 2888 = 2^{3} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2888.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(1.44129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 152) |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.2888.1 |
Artin image: | $S_3$ |
Artin field: | Galois closure of 3.1.2888.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times\).
\(n\) | \(1445\) | \(2167\) | \(2529\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
723.1 |
|
1.00000 | −1.00000 | 1.00000 | 0 | −1.00000 | 0 | 1.00000 | 0 | 0 | |||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
8.d | odd | 2 | 1 | CM by \(\Q(\sqrt{-2}) \) |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2888.1.f.b | 1 | |
8.d | odd | 2 | 1 | CM | 2888.1.f.b | 1 | |
19.b | odd | 2 | 1 | 2888.1.f.a | 1 | ||
19.c | even | 3 | 2 | 152.1.k.a | ✓ | 2 | |
19.d | odd | 6 | 2 | 2888.1.k.a | 2 | ||
19.e | even | 9 | 6 | 2888.1.u.c | 6 | ||
19.f | odd | 18 | 6 | 2888.1.u.d | 6 | ||
57.h | odd | 6 | 2 | 1368.1.bz.a | 2 | ||
76.g | odd | 6 | 2 | 608.1.o.a | 2 | ||
95.i | even | 6 | 2 | 3800.1.bd.c | 2 | ||
95.m | odd | 12 | 4 | 3800.1.bn.b | 4 | ||
152.b | even | 2 | 1 | 2888.1.f.a | 1 | ||
152.k | odd | 6 | 2 | 152.1.k.a | ✓ | 2 | |
152.o | even | 6 | 2 | 2888.1.k.a | 2 | ||
152.p | even | 6 | 2 | 608.1.o.a | 2 | ||
152.u | odd | 18 | 6 | 2888.1.u.c | 6 | ||
152.v | even | 18 | 6 | 2888.1.u.d | 6 | ||
456.u | even | 6 | 2 | 1368.1.bz.a | 2 | ||
760.bm | odd | 6 | 2 | 3800.1.bd.c | 2 | ||
760.bw | even | 12 | 4 | 3800.1.bn.b | 4 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
152.1.k.a | ✓ | 2 | 19.c | even | 3 | 2 | |
152.1.k.a | ✓ | 2 | 152.k | odd | 6 | 2 | |
608.1.o.a | 2 | 76.g | odd | 6 | 2 | ||
608.1.o.a | 2 | 152.p | even | 6 | 2 | ||
1368.1.bz.a | 2 | 57.h | odd | 6 | 2 | ||
1368.1.bz.a | 2 | 456.u | even | 6 | 2 | ||
2888.1.f.a | 1 | 19.b | odd | 2 | 1 | ||
2888.1.f.a | 1 | 152.b | even | 2 | 1 | ||
2888.1.f.b | 1 | 1.a | even | 1 | 1 | trivial | |
2888.1.f.b | 1 | 8.d | odd | 2 | 1 | CM | |
2888.1.k.a | 2 | 19.d | odd | 6 | 2 | ||
2888.1.k.a | 2 | 152.o | even | 6 | 2 | ||
2888.1.u.c | 6 | 19.e | even | 9 | 6 | ||
2888.1.u.c | 6 | 152.u | odd | 18 | 6 | ||
2888.1.u.d | 6 | 19.f | odd | 18 | 6 | ||
2888.1.u.d | 6 | 152.v | even | 18 | 6 | ||
3800.1.bd.c | 2 | 95.i | even | 6 | 2 | ||
3800.1.bd.c | 2 | 760.bm | odd | 6 | 2 | ||
3800.1.bn.b | 4 | 95.m | odd | 12 | 4 | ||
3800.1.bn.b | 4 | 760.bw | even | 12 | 4 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 1 \)
acting on \(S_{1}^{\mathrm{new}}(2888, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 1 \)
$3$
\( T + 1 \)
$5$
\( T \)
$7$
\( T \)
$11$
\( T + 1 \)
$13$
\( T \)
$17$
\( T - 2 \)
$19$
\( T \)
$23$
\( T \)
$29$
\( T \)
$31$
\( T \)
$37$
\( T \)
$41$
\( T + 1 \)
$43$
\( T - 2 \)
$47$
\( T \)
$53$
\( T \)
$59$
\( T + 1 \)
$61$
\( T \)
$67$
\( T + 1 \)
$71$
\( T \)
$73$
\( T + 1 \)
$79$
\( T \)
$83$
\( T + 1 \)
$89$
\( T - 2 \)
$97$
\( T + 1 \)
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