Newspace parameters
| Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1932.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(113.991690131\) |
| Analytic rank: | \(0\) |
| Dimension: | \(3\) |
| Coefficient field: | 3.3.660841.1 |
|
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
| Defining polynomial: |
\( x^{3} - x^{2} - 186x - 216 \)
|
| Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
| 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
\( x^{3} - x^{2} - 186x - 216 \)
:
| \(\beta_{1}\) | \(=\) |
\( \nu \)
|
| \(\beta_{2}\) | \(=\) |
\( ( \nu^{2} - \nu - 126 ) / 6 \)
|
| \(\nu\) | \(=\) |
\( \beta_1 \)
|
| \(\nu^{2}\) | \(=\) |
\( 6\beta_{2} + \beta _1 + 126 \)
|
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 |
|
0 | −3.00000 | 0 | −14.5727 | 0 | 7.00000 | 0 | 9.00000 | 0 | |||||||||||||||||||||||||||
| 1.2 | 0 | −3.00000 | 0 | 13.1197 | 0 | 7.00000 | 0 | 9.00000 | 0 | ||||||||||||||||||||||||||||
| 1.3 | 0 | −3.00000 | 0 | 18.4529 | 0 | 7.00000 | 0 | 9.00000 | 0 | ||||||||||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \(-1\) |
| \(3\) | \(1\) |
| \(7\) | \(-1\) |
| \(23\) | \(1\) |
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 | 1932.4.a.d | ✓ | 3 |
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 1932.4.a.d | ✓ | 3 | 1.a | even | 1 | 1 | trivial |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{5}^{3} - 17T_{5}^{2} - 218T_{5} + 3528 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1932))\).
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T^{3} \)
|
| $3$ |
\( (T + 3)^{3} \)
|
| $5$ |
\( T^{3} - 17 T^{2} + \cdots + 3528 \)
|
| $7$ |
\( (T - 7)^{3} \)
|
| $11$ |
\( T^{3} + 55 T^{2} + \cdots - 21168 \)
|
| $13$ |
\( T^{3} + 67 T^{2} + \cdots - 244 \)
|
| $17$ |
\( T^{3} + 46 T^{2} + \cdots + 77856 \)
|
| $19$ |
\( T^{3} + 137 T^{2} + \cdots - 144032 \)
|
| $23$ |
\( (T + 23)^{3} \)
|
| $29$ |
\( T^{3} + 377 T^{2} + \cdots - 949092 \)
|
| $31$ |
\( T^{3} - 336 T^{2} + \cdots + 5495808 \)
|
| $37$ |
\( T^{3} - 347 T^{2} + \cdots + 1395452 \)
|
| $41$ |
\( T^{3} + 326 T^{2} + \cdots - 11348694 \)
|
| $43$ |
\( T^{3} + 15 T^{2} + \cdots - 13165392 \)
|
| $47$ |
\( T^{3} - 300 T^{2} + \cdots - 1947888 \)
|
| $53$ |
\( T^{3} - 407 T^{2} + \cdots - 610776 \)
|
| $59$ |
\( T^{3} - 915 T^{2} + \cdots + 185189976 \)
|
| $61$ |
\( T^{3} + 939 T^{2} + \cdots - 142394268 \)
|
| $67$ |
\( T^{3} + 1012 T^{2} + \cdots - 212506432 \)
|
| $71$ |
\( T^{3} - 2890 T^{2} + \cdots - 883161216 \)
|
| $73$ |
\( T^{3} - 802 T^{2} + \cdots + 40251648 \)
|
| $79$ |
\( T^{3} + 802 T^{2} + \cdots - 226374912 \)
|
| $83$ |
\( T^{3} - 6 T^{2} + \cdots + 598989216 \)
|
| $89$ |
\( T^{3} - 954 T^{2} + \cdots - 104806872 \)
|
| $97$ |
\( T^{3} - 157 T^{2} + \cdots + 46173084 \)
|
| show more | |
| show less |