Newspace parameters
Level: | \( N \) | \(=\) | \( 465 = 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 465.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(3.71304369399\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{3}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
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 \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.
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 |
|
−1.73205 | −1.00000 | 1.00000 | −1.00000 | 1.73205 | −1.26795 | 1.73205 | 1.00000 | 1.73205 | ||||||||||||||||||||||||
1.2 | 1.73205 | −1.00000 | 1.00000 | −1.00000 | −1.73205 | −4.73205 | −1.73205 | 1.00000 | −1.73205 | |||||||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(5\) | \(1\) |
\(31\) | \(1\) |
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 | 465.2.a.d | ✓ | 2 |
3.b | odd | 2 | 1 | 1395.2.a.f | 2 | ||
4.b | odd | 2 | 1 | 7440.2.a.bk | 2 | ||
5.b | even | 2 | 1 | 2325.2.a.m | 2 | ||
5.c | odd | 4 | 2 | 2325.2.c.j | 4 | ||
15.d | odd | 2 | 1 | 6975.2.a.v | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
465.2.a.d | ✓ | 2 | 1.a | even | 1 | 1 | trivial |
1395.2.a.f | 2 | 3.b | odd | 2 | 1 | ||
2325.2.a.m | 2 | 5.b | even | 2 | 1 | ||
2325.2.c.j | 4 | 5.c | odd | 4 | 2 | ||
6975.2.a.v | 2 | 15.d | odd | 2 | 1 | ||
7440.2.a.bk | 2 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - 3 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(465))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T^{2} - 3 \)
$3$
\( (T + 1)^{2} \)
$5$
\( (T + 1)^{2} \)
$7$
\( T^{2} + 6T + 6 \)
$11$
\( T^{2} - 4T - 8 \)
$13$
\( T^{2} + 6T + 6 \)
$17$
\( T^{2} - 4T - 8 \)
$19$
\( T^{2} - 4T - 8 \)
$23$
\( T^{2} + 8T + 4 \)
$29$
\( T^{2} + 2T - 2 \)
$31$
\( (T + 1)^{2} \)
$37$
\( T^{2} + 10T + 22 \)
$41$
\( T^{2} - 12 \)
$43$
\( (T + 4)^{2} \)
$47$
\( (T + 6)^{2} \)
$53$
\( T^{2} - 4T - 104 \)
$59$
\( T^{2} + 14T + 22 \)
$61$
\( T^{2} - 108 \)
$67$
\( T^{2} + 10T - 2 \)
$71$
\( T^{2} + 18T + 54 \)
$73$
\( T^{2} + 6T - 66 \)
$79$
\( (T + 10)^{2} \)
$83$
\( T^{2} - 24T + 132 \)
$89$
\( T^{2} - 18T + 78 \)
$97$
\( (T + 2)^{2} \)
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