Newspace parameters
| Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 483.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(28.4979225328\) |
| Analytic rank: | \(1\) |
| Dimension: | \(3\) |
| Coefficient field: | 3.3.3877.1 |
|
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
| Defining polynomial: |
\( x^{3} - x^{2} - 13x - 10 \)
|
| 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 \(1,\beta_1,\beta_2\) 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
\( x^{3} - x^{2} - 13x - 10 \)
:
| \(\beta_{1}\) | \(=\) |
\( \nu \)
|
| \(\beta_{2}\) | \(=\) |
\( \nu^{2} - 2\nu - 8 \)
|
| \(\nu\) | \(=\) |
\( \beta_1 \)
|
| \(\nu^{2}\) | \(=\) |
\( \beta_{2} + 2\beta _1 + 8 \)
|
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 |
|
−5.43745 | 3.00000 | 21.5659 | −5.05882 | −16.3124 | −7.00000 | −73.7640 | 9.00000 | 27.5071 | |||||||||||||||||||||||||||
| 1.2 | −0.118219 | 3.00000 | −7.98602 | −2.69534 | −0.354656 | −7.00000 | 1.88985 | 9.00000 | 0.318639 | ||||||||||||||||||||||||||||
| 1.3 | 1.55567 | 3.00000 | −5.57988 | 9.75415 | 4.66702 | −7.00000 | −21.1259 | 9.00000 | 15.1743 | ||||||||||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(3\) | \(-1\) |
| \(7\) | \(1\) |
| \(23\) | \(1\) |
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 | 483.4.a.a | ✓ | 3 |
| 3.b | odd | 2 | 1 | 1449.4.a.c | 3 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 483.4.a.a | ✓ | 3 | 1.a | even | 1 | 1 | trivial |
| 1449.4.a.c | 3 | 3.b | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{3} + 4T_{2}^{2} - 8T_{2} - 1 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(483))\).
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T^{3} + 4 T^{2} + \cdots - 1 \)
|
| $3$ |
\( (T - 3)^{3} \)
|
| $5$ |
\( T^{3} - 2 T^{2} + \cdots - 133 \)
|
| $7$ |
\( (T + 7)^{3} \)
|
| $11$ |
\( T^{3} - 4 T^{2} + \cdots + 16888 \)
|
| $13$ |
\( T^{3} - 32 T^{2} + \cdots + 7121 \)
|
| $17$ |
\( T^{3} + 86 T^{2} + \cdots - 32140 \)
|
| $19$ |
\( T^{3} - 32 T^{2} + \cdots - 4436 \)
|
| $23$ |
\( (T + 23)^{3} \)
|
| $29$ |
\( T^{3} + 341 T^{2} + \cdots + 1279711 \)
|
| $31$ |
\( T^{3} + 452 T^{2} + \cdots + 2969438 \)
|
| $37$ |
\( T^{3} + 183 T^{2} + \cdots - 3177991 \)
|
| $41$ |
\( T^{3} - 175 T^{2} + \cdots + 11602699 \)
|
| $43$ |
\( T^{3} + 320 T^{2} + \cdots - 3480943 \)
|
| $47$ |
\( T^{3} + 71 T^{2} + \cdots - 30926812 \)
|
| $53$ |
\( T^{3} - 27 T^{2} + \cdots + 9069176 \)
|
| $59$ |
\( T^{3} + 1585 T^{2} + \cdots + 57554534 \)
|
| $61$ |
\( T^{3} + 449 T^{2} + \cdots - 11531794 \)
|
| $67$ |
\( T^{3} + 239 T^{2} + \cdots - 90556772 \)
|
| $71$ |
\( T^{3} - 1255 T^{2} + \cdots + 7078618 \)
|
| $73$ |
\( T^{3} + 342 T^{2} + \cdots + 20669796 \)
|
| $79$ |
\( T^{3} - 994 T^{2} + \cdots + 161629604 \)
|
| $83$ |
\( T^{3} + 1846 T^{2} + \cdots - 147725860 \)
|
| $89$ |
\( T^{3} + \cdots - 1448227670 \)
|
| $97$ |
\( T^{3} + 1797 T^{2} + \cdots + 26418199 \)
|
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