Newspace parameters
| Level: | \( N \) | \(=\) | \( 190 = 2 \cdot 5 \cdot 19 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 190.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(11.2103629011\) |
| Analytic rank: | \(1\) |
| Dimension: | \(3\) |
| Coefficient field: | 3.3.5468.1 |
|
|
|
| Defining polynomial: |
\( x^{3} - 23x - 40 \)
|
| Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
| 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
\( x^{3} - 23x - 40 \)
:
| \(\beta_{1}\) | \(=\) |
\( \nu \)
|
| \(\beta_{2}\) | \(=\) |
\( \nu^{2} - 3\nu - 15 \)
|
| \(\nu\) | \(=\) |
\( \beta_1 \)
|
| \(\nu^{2}\) | \(=\) |
\( \beta_{2} + 3\beta _1 + 15 \)
|
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 |
|
2.00000 | −8.50184 | 4.00000 | −5.00000 | −17.0037 | 33.2777 | 8.00000 | 45.2814 | −10.0000 | |||||||||||||||||||||||||||
| 1.2 | 2.00000 | −0.794314 | 4.00000 | −5.00000 | −1.58863 | −22.9577 | 8.00000 | −26.3691 | −10.0000 | ||||||||||||||||||||||||||||
| 1.3 | 2.00000 | 0.296159 | 4.00000 | −5.00000 | 0.592317 | −21.3200 | 8.00000 | −26.9123 | −10.0000 | ||||||||||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(2\) | \( -1 \) |
| \(5\) | \( +1 \) |
| \(19\) | \( +1 \) |
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 | 190.4.a.h | ✓ | 3 |
| 3.b | odd | 2 | 1 | 1710.4.a.x | 3 | ||
| 4.b | odd | 2 | 1 | 1520.4.a.p | 3 | ||
| 5.b | even | 2 | 1 | 950.4.a.m | 3 | ||
| 5.c | odd | 4 | 2 | 950.4.b.j | 6 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 190.4.a.h | ✓ | 3 | 1.a | even | 1 | 1 | trivial |
| 950.4.a.m | 3 | 5.b | even | 2 | 1 | ||
| 950.4.b.j | 6 | 5.c | odd | 4 | 2 | ||
| 1520.4.a.p | 3 | 4.b | odd | 2 | 1 | ||
| 1710.4.a.x | 3 | 3.b | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{3} + 9T_{3}^{2} + 4T_{3} - 2 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(190))\).
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( (T - 2)^{3} \)
|
| $3$ |
\( T^{3} + 9 T^{2} + \cdots - 2 \)
|
| $5$ |
\( (T + 5)^{3} \)
|
| $7$ |
\( T^{3} + 11 T^{2} + \cdots - 16288 \)
|
| $11$ |
\( T^{3} + 68 T^{2} + \cdots - 194816 \)
|
| $13$ |
\( T^{3} + 121 T^{2} + \cdots + 942 \)
|
| $17$ |
\( T^{3} + 103 T^{2} + \cdots - 1782324 \)
|
| $19$ |
\( (T + 19)^{3} \)
|
| $23$ |
\( T^{3} + 203 T^{2} + \cdots - 2255976 \)
|
| $29$ |
\( T^{3} - 91 T^{2} + \cdots + 61620 \)
|
| $31$ |
\( T^{3} + 154 T^{2} + \cdots - 2514272 \)
|
| $37$ |
\( T^{3} + 304 T^{2} + \cdots - 3608532 \)
|
| $41$ |
\( T^{3} - 282 T^{2} + \cdots - 749864 \)
|
| $43$ |
\( T^{3} + 214 T^{2} + \cdots - 14445824 \)
|
| $47$ |
\( T^{3} + 1144 T^{2} + \cdots + 51801600 \)
|
| $53$ |
\( T^{3} - 795 T^{2} + \cdots + 7559654 \)
|
| $59$ |
\( T^{3} + 609 T^{2} + \cdots - 12873880 \)
|
| $61$ |
\( T^{3} - 792 T^{2} + \cdots - 6609824 \)
|
| $67$ |
\( T^{3} + 865 T^{2} + \cdots - 57516042 \)
|
| $71$ |
\( T^{3} + 312 T^{2} + \cdots - 40935424 \)
|
| $73$ |
\( T^{3} - 79 T^{2} + \cdots + 356614884 \)
|
| $79$ |
\( T^{3} - 1806 T^{2} + \cdots - 89460880 \)
|
| $83$ |
\( T^{3} + 34 T^{2} + \cdots - 212872272 \)
|
| $89$ |
\( T^{3} + \cdots - 1232043000 \)
|
| $97$ |
\( T^{3} + 1120 T^{2} + \cdots + 38577204 \)
|
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