Newspace parameters
| Level: | \( N \) | = | \( 225 = 3^{2} \cdot 5^{2} \) |
| Weight: | \( k \) | = | \( 2 \) |
| Character orbit: | \([\chi]\) | = | 225.a (trivial) |
Newform invariants
| Self dual: | Yes |
| Analytic conductor: | \(1.79663404548\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Fricke sign: | \(-1\) |
| Sato-Tate group: | $N(\mathrm{U}(1))$ |
$q$-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 | 0 | −2.00000 | 0 | 0 | 5.00000 | 0 | 0 | 0 | |||||||||||||||||||||
Inner twists
| Char. orbit | Parity | Mult. | Self Twist | Proved |
|---|---|---|---|---|
| 1.a | Even | 1 | trivial | yes |
| 3.b | Odd | 1 | CM by \(\Q(\sqrt{-3}) \) | yes |
Atkin-Lehner signs
| \( p \) | Sign |
|---|---|
| \(3\) | \(1\) |
| \(5\) | \(-1\) |
Hecke kernels
This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(225))\):
| \(T_{2} \) |
| \(T_{7} \) \(\mathstrut -\mathstrut 5 \) |