Newspace parameters
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(48.1151459439\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
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 | 9.00000 | 0 | 0 | 0 | 91.0000 | 0 | 81.0000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(-1\) |
\(3\) | \(-1\) |
\(5\) | \(1\) |
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 | 300.6.a.f | yes | 1 |
3.b | odd | 2 | 1 | 900.6.a.i | 1 | ||
5.b | even | 2 | 1 | 300.6.a.a | ✓ | 1 | |
5.c | odd | 4 | 2 | 300.6.d.b | 2 | ||
15.d | odd | 2 | 1 | 900.6.a.d | 1 | ||
15.e | even | 4 | 2 | 900.6.d.g | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
300.6.a.a | ✓ | 1 | 5.b | even | 2 | 1 | |
300.6.a.f | yes | 1 | 1.a | even | 1 | 1 | trivial |
300.6.d.b | 2 | 5.c | odd | 4 | 2 | ||
900.6.a.d | 1 | 15.d | odd | 2 | 1 | ||
900.6.a.i | 1 | 3.b | odd | 2 | 1 | ||
900.6.d.g | 2 | 15.e | even | 4 | 2 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{7} - 91 \)
acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(300))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T \)
$3$
\( T - 9 \)
$5$
\( T \)
$7$
\( T - 91 \)
$11$
\( T + 174 \)
$13$
\( T + 785 \)
$17$
\( T + 1794 \)
$19$
\( T + 925 \)
$23$
\( T - 2346 \)
$29$
\( T + 726 \)
$31$
\( T + 811 \)
$37$
\( T + 7922 \)
$41$
\( T + 360 \)
$43$
\( T - 4951 \)
$47$
\( T + 9906 \)
$53$
\( T - 8292 \)
$59$
\( T - 7014 \)
$61$
\( T + 51433 \)
$67$
\( T + 581 \)
$71$
\( T + 56520 \)
$73$
\( T - 42478 \)
$79$
\( T + 28912 \)
$83$
\( T - 104586 \)
$89$
\( T + 118080 \)
$97$
\( T + 110273 \)
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