Newspace parameters
| Level: | \( N \) | = | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Character orbit: | \([\chi]\) | = | 276.h (of order \(2\) and degree \(1\)) |
Newform invariants
| Self dual: | Yes |
| Analytic conductor: | \(0.137741943487\) |
| Analytic rank: | \(0\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Projective image | \(D_{2}\) |
| Projective field | Galois closure of \(\Q(\sqrt{3}, \sqrt{-23})\) |
| Artin image size | \(8\) |
| Artin image | $D_4$ |
| Artin field | Galois closure of 4.2.3312.1 |
$q$-expansion
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
| \(n\) | \(97\) | \(139\) | \(185\) |
| \(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 275.1 |
|
1.00000 | −1.00000 | 1.00000 | 0 | −1.00000 | 0 | 1.00000 | 1.00000 | 0 | |||||||||||||||||||||
Inner twists
| Char. orbit | Parity | Mult. | Self Twist | Proved |
|---|---|---|---|---|
| 1.a | Even | 1 | trivial | yes |
| 12.b | Even | 1 | RM by \(\Q(\sqrt{3}) \) | yes |
| 23.b | Odd | 1 | CM by \(\Q(\sqrt{-23}) \) | yes |
| 276.h | Odd | 1 | CM by \(\Q(\sqrt{-69}) \) | yes |
Hecke kernels
This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(276, [\chi])\):
| \( T_{13} + 2 \) |
| \( T_{47} - 2 \) |