Newspace parameters
| Level: | \( N \) | \(=\) | \( 2883 = 3 \cdot 31^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 2883.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(23.0208709027\) |
| Analytic rank: | \(0\) |
| Dimension: | \(4\) |
| Coefficient field: | 4.4.8768.1 |
|
|
|
| Defining polynomial: |
\( x^{4} - 2x^{3} - 5x^{2} + 6x + 7 \)
|
| Coefficient ring: | \(\Z[a_1, a_2]\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | yes |
| Fricke sign: | \(-1\) |
| Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2,\beta_3\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of
\( x^{4} - 2x^{3} - 5x^{2} + 6x + 7 \)
:
| \(\beta_{1}\) | \(=\) |
\( \nu \)
|
| \(\beta_{2}\) | \(=\) |
\( \nu^{2} - \nu - 3 \)
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| \(\beta_{3}\) | \(=\) |
\( \nu^{3} - \nu^{2} - 4\nu \)
|
| \(\nu\) | \(=\) |
\( \beta_1 \)
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| \(\nu^{2}\) | \(=\) |
\( \beta_{2} + \beta _1 + 3 \)
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| \(\nu^{3}\) | \(=\) |
\( \beta_{3} + \beta_{2} + 5\beta _1 + 3 \)
|
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1.1 |
|
−2.65968 | −1.00000 | 5.07389 | 3.34714 | 2.65968 | −1.00000 | −8.17557 | 1.00000 | −8.90232 | ||||||||||||||||||||||||||||||
| 1.2 | −1.85491 | −1.00000 | 1.44070 | −0.209028 | 1.85491 | −1.00000 | 1.03746 | 1.00000 | 0.387729 | |||||||||||||||||||||||||||||||
| 1.3 | 0.854912 | −1.00000 | −1.26913 | 3.62324 | −0.854912 | −1.00000 | −2.79481 | 1.00000 | 3.09755 | |||||||||||||||||||||||||||||||
| 1.4 | 1.65968 | −1.00000 | 0.754535 | −2.76135 | −1.65968 | −1.00000 | −2.06707 | 1.00000 | −4.58296 | |||||||||||||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(3\) | \( +1 \) |
| \(31\) | \( -1 \) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
| By twisting character orbit | |||||||
|---|---|---|---|---|---|---|---|
| Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
| 1.a | even | 1 | 1 | trivial | 2883.2.a.i | ✓ | 4 |
| 3.b | odd | 2 | 1 | 8649.2.a.z | 4 | ||
| 31.b | odd | 2 | 1 | 2883.2.a.j | yes | 4 | |
| 93.c | even | 2 | 1 | 8649.2.a.y | 4 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 2883.2.a.i | ✓ | 4 | 1.a | even | 1 | 1 | trivial |
| 2883.2.a.j | yes | 4 | 31.b | odd | 2 | 1 | |
| 8649.2.a.y | 4 | 93.c | even | 2 | 1 | ||
| 8649.2.a.z | 4 | 3.b | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2883))\):
|
\( T_{2}^{4} + 2T_{2}^{3} - 5T_{2}^{2} - 6T_{2} + 7 \)
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\( T_{11}^{4} - 22T_{11}^{2} + 24T_{11} - 4 \)
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\( T_{13}^{4} - 8T_{13}^{3} + 10T_{13}^{2} + 32T_{13} - 28 \)
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Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T^{4} + 2 T^{3} + \cdots + 7 \)
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| $3$ |
\( (T + 1)^{4} \)
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| $5$ |
\( T^{4} - 4 T^{3} + \cdots + 7 \)
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| $7$ |
\( (T + 1)^{4} \)
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| $11$ |
\( T^{4} - 22 T^{2} + \cdots - 4 \)
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| $13$ |
\( T^{4} - 8 T^{3} + \cdots - 28 \)
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| $17$ |
\( (T^{2} - 8 T + 8)^{2} \)
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| $19$ |
\( T^{4} + 8 T^{3} + \cdots - 359 \)
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| $23$ |
\( T^{4} + 4 T^{3} + \cdots - 164 \)
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| $29$ |
\( T^{4} - 8 T^{3} + \cdots + 1244 \)
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| $31$ |
\( T^{4} \)
|
| $37$ |
\( T^{4} - 24 T^{3} + \cdots - 284 \)
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| $41$ |
\( T^{4} - 24 T^{3} + \cdots + 287 \)
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| $43$ |
\( T^{4} - 8 T^{3} + \cdots + 196 \)
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| $47$ |
\( T^{4} + 16 T^{3} + \cdots - 1984 \)
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| $53$ |
\( (T^{2} - 8 T + 8)^{2} \)
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| $59$ |
\( T^{4} - 4 T^{3} + \cdots + 1519 \)
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| $61$ |
\( T^{4} - 8 T^{3} + \cdots + 1792 \)
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| $67$ |
\( T^{4} + 8 T^{3} + \cdots - 1792 \)
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| $71$ |
\( T^{4} - 4 T^{3} + \cdots + 199 \)
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| $73$ |
\( T^{4} + 16 T^{3} + \cdots - 6076 \)
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| $79$ |
\( T^{4} - 212 T^{2} + \cdots + 8356 \)
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| $83$ |
\( T^{4} - 12 T^{3} + \cdots - 1316 \)
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| $89$ |
\( T^{4} - 28 T^{3} + \cdots + 796 \)
|
| $97$ |
\( T^{4} + 12 T^{3} + \cdots - 7 \)
|
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