Newspace parameters
Level: | \( N \) | \(=\) | \( 1156 = 2^{2} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1156.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(9.23070647366\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
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 \(\beta = \frac{1}{2}(1 + \sqrt{21})\). 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 |
|
0 | −2.79129 | 0 | −3.79129 | 0 | −0.208712 | 0 | 4.79129 | 0 | ||||||||||||||||||||||||
1.2 | 0 | 1.79129 | 0 | 0.791288 | 0 | −4.79129 | 0 | 0.208712 | 0 | |||||||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(17\) | \(-1\) |
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 | 1156.2.a.b | ✓ | 2 |
4.b | odd | 2 | 1 | 4624.2.a.u | 2 | ||
17.b | even | 2 | 1 | 1156.2.a.d | yes | 2 | |
17.c | even | 4 | 2 | 1156.2.b.b | 4 | ||
17.d | even | 8 | 4 | 1156.2.e.e | 8 | ||
17.e | odd | 16 | 8 | 1156.2.h.g | 16 | ||
68.d | odd | 2 | 1 | 4624.2.a.k | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
1156.2.a.b | ✓ | 2 | 1.a | even | 1 | 1 | trivial |
1156.2.a.d | yes | 2 | 17.b | even | 2 | 1 | |
1156.2.b.b | 4 | 17.c | even | 4 | 2 | ||
1156.2.e.e | 8 | 17.d | even | 8 | 4 | ||
1156.2.h.g | 16 | 17.e | odd | 16 | 8 | ||
4624.2.a.k | 2 | 68.d | odd | 2 | 1 | ||
4624.2.a.u | 2 | 4.b | odd | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3}^{2} + T_{3} - 5 \)
acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T^{2} \)
$3$
\( T^{2} + T - 5 \)
$5$
\( T^{2} + 3T - 3 \)
$7$
\( T^{2} + 5T + 1 \)
$11$
\( T^{2} - 21 \)
$13$
\( T^{2} - T - 5 \)
$17$
\( T^{2} \)
$19$
\( T^{2} + 5T + 1 \)
$23$
\( T^{2} - 9T + 15 \)
$29$
\( T^{2} + 15T + 51 \)
$31$
\( (T - 5)^{2} \)
$37$
\( T^{2} + 2T - 20 \)
$41$
\( (T + 6)^{2} \)
$43$
\( (T + 1)^{2} \)
$47$
\( T^{2} - 12T + 15 \)
$53$
\( T^{2} + 9T + 15 \)
$59$
\( T^{2} - 84 \)
$61$
\( T^{2} + 20T + 79 \)
$67$
\( T^{2} + 2T - 20 \)
$71$
\( (T - 6)^{2} \)
$73$
\( T^{2} - 4T - 185 \)
$79$
\( (T - 2)^{2} \)
$83$
\( T^{2} - 9T + 15 \)
$89$
\( T^{2} - 84 \)
$97$
\( T^{2} - T - 131 \)
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