Newspace parameters
Level: | \( N \) | \(=\) | \( 3751 = 11^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3751.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(1.87199286239\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 31) |
Projective image: | \(D_{3}\) |
Projective field: | Galois closure of 3.1.31.1 |
Artin image: | $D_6$ |
Artin field: | Galois closure of 6.0.1279091.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3751\mathbb{Z}\right)^\times\).
\(n\) | \(2421\) | \(2543\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1332.1 |
|
1.00000 | 0 | 0 | −1.00000 | 0 | 1.00000 | −1.00000 | 1.00000 | −1.00000 | |||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
31.b | odd | 2 | 1 | CM by \(\Q(\sqrt{-31}) \) |
Twists
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 1 \)
acting on \(S_{1}^{\mathrm{new}}(3751, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 1 \)
$3$
\( T \)
$5$
\( T + 1 \)
$7$
\( T - 1 \)
$11$
\( T \)
$13$
\( T \)
$17$
\( T \)
$19$
\( T - 1 \)
$23$
\( T \)
$29$
\( T \)
$31$
\( T - 1 \)
$37$
\( T \)
$41$
\( T - 1 \)
$43$
\( T \)
$47$
\( T - 2 \)
$53$
\( T \)
$59$
\( T + 1 \)
$61$
\( T \)
$67$
\( T - 2 \)
$71$
\( T + 1 \)
$73$
\( T \)
$79$
\( T \)
$83$
\( T \)
$89$
\( T \)
$97$
\( T + 1 \)
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