Newspace parameters
| Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 1805.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(14.4129975648\) |
| Analytic rank: | \(0\) |
| Dimension: | \(4\) |
| Coefficient field: | 4.4.7537.1 |
|
|
|
| Defining polynomial: |
\( x^{4} - x^{3} - 5x^{2} + 4x + 3 \)
|
| Coefficient ring: | \(\Z[a_1, a_2]\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 95) |
| 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
\( x^{4} - x^{3} - 5x^{2} + 4x + 3 \)
:
| \(\beta_{1}\) | \(=\) |
\( \nu \)
|
| \(\beta_{2}\) | \(=\) |
\( \nu^{2} - 3 \)
|
| \(\beta_{3}\) | \(=\) |
\( \nu^{3} - 4\nu \)
|
| \(\nu\) | \(=\) |
\( \beta_1 \)
|
| \(\nu^{2}\) | \(=\) |
\( \beta_{2} + 3 \)
|
| \(\nu^{3}\) | \(=\) |
\( \beta_{3} + 4\beta_1 \)
|
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1.1 |
|
−1.66454 | −1.15976 | 0.770710 | 1.00000 | 1.93047 | −2.43525 | 2.04621 | −1.65497 | −1.66454 | ||||||||||||||||||||||||||||||
| 1.2 | −1.19091 | 3.04717 | −0.581734 | 1.00000 | −3.62891 | −0.609175 | 3.07461 | 6.28525 | −1.19091 | |||||||||||||||||||||||||||||||
| 1.3 | 1.09744 | −0.379334 | −0.795629 | 1.00000 | −0.416295 | 1.89307 | −3.06803 | −2.85611 | 1.09744 | |||||||||||||||||||||||||||||||
| 1.4 | 2.75802 | 1.49192 | 5.60665 | 1.00000 | 4.11474 | −2.84864 | 9.94721 | −0.774179 | 2.75802 | |||||||||||||||||||||||||||||||
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(5\) | \( -1 \) |
| \(19\) | \( +1 \) |
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 | 1805.2.a.o | 4 | |
| 5.b | even | 2 | 1 | 9025.2.a.bg | 4 | ||
| 19.b | odd | 2 | 1 | 1805.2.a.i | 4 | ||
| 19.c | even | 3 | 2 | 95.2.e.c | ✓ | 8 | |
| 57.h | odd | 6 | 2 | 855.2.k.h | 8 | ||
| 76.g | odd | 6 | 2 | 1520.2.q.o | 8 | ||
| 95.d | odd | 2 | 1 | 9025.2.a.bp | 4 | ||
| 95.i | even | 6 | 2 | 475.2.e.e | 8 | ||
| 95.m | odd | 12 | 4 | 475.2.j.c | 16 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 95.2.e.c | ✓ | 8 | 19.c | even | 3 | 2 | |
| 475.2.e.e | 8 | 95.i | even | 6 | 2 | ||
| 475.2.j.c | 16 | 95.m | odd | 12 | 4 | ||
| 855.2.k.h | 8 | 57.h | odd | 6 | 2 | ||
| 1520.2.q.o | 8 | 76.g | odd | 6 | 2 | ||
| 1805.2.a.i | 4 | 19.b | odd | 2 | 1 | ||
| 1805.2.a.o | 4 | 1.a | even | 1 | 1 | trivial | |
| 9025.2.a.bg | 4 | 5.b | even | 2 | 1 | ||
| 9025.2.a.bp | 4 | 95.d | odd | 2 | 1 | ||
Hecke kernels
This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\):
|
\( T_{2}^{4} - T_{2}^{3} - 6T_{2}^{2} + T_{2} + 6 \)
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\( T_{3}^{4} - 3T_{3}^{3} - 2T_{3}^{2} + 5T_{3} + 2 \)
|
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ |
\( T^{4} - T^{3} - 6 T^{2} + \cdots + 6 \)
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| $3$ |
\( T^{4} - 3 T^{3} + \cdots + 2 \)
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| $5$ |
\( (T - 1)^{4} \)
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| $7$ |
\( T^{4} + 4 T^{3} + \cdots - 8 \)
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| $11$ |
\( T^{4} + 2 T^{3} + \cdots + 3 \)
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| $13$ |
\( T^{4} - 7 T^{3} + \cdots - 16 \)
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| $17$ |
\( T^{4} + T^{3} + \cdots + 108 \)
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| $19$ |
\( T^{4} \)
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| $23$ |
\( T^{4} - 2 T^{3} + \cdots + 6 \)
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| $29$ |
\( T^{4} + T^{3} + \cdots - 141 \)
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| $31$ |
\( T^{4} - 67 T^{2} + \cdots + 1063 \)
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| $37$ |
\( T^{4} + 2 T^{3} + \cdots - 118 \)
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| $41$ |
\( T^{4} + 8 T^{3} + \cdots - 2238 \)
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| $43$ |
\( T^{4} - T^{3} + \cdots + 794 \)
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| $47$ |
\( T^{4} + 12 T^{3} + \cdots - 2316 \)
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| $53$ |
\( T^{4} + 5 T^{3} + \cdots - 54 \)
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| $59$ |
\( T^{4} + 5 T^{3} + \cdots + 1875 \)
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| $61$ |
\( T^{4} - 130 T^{2} + \cdots + 3049 \)
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| $67$ |
\( T^{4} - 4 T^{3} + \cdots + 64 \)
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| $71$ |
\( T^{4} - 20 T^{3} + \cdots - 243 \)
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| $73$ |
\( T^{4} + 20 T^{3} + \cdots - 1726 \)
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| $79$ |
\( T^{4} - 17 T^{3} + \cdots - 184 \)
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| $83$ |
\( T^{4} - T^{3} + \cdots + 366 \)
|
| $89$ |
\( T^{4} - 11 T^{3} + \cdots - 3816 \)
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| $97$ |
\( T^{4} - T^{3} + \cdots + 7442 \)
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