Newspace parameters
Level: | \( N \) | = | \( 2 \) |
Weight: | \( k \) | = | \( 48 \) |
Character orbit: | \([\chi]\) | = | 2.a (trivial) |
Newform invariants
Self dual: | Yes |
Analytic conductor: | \(27.981532531\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{3}\cdot 5 \) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 8640\sqrt{23589383914321}\). 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 |
|
−8.38861e6 | −1.48673e11 | 7.03687e13 | 2.84306e16 | 1.24716e18 | 5.21750e19 | −5.90296e20 | −4.48523e21 | −2.38493e23 | ||||||||||||||||||||||||
1.2 | −8.38861e6 | 2.70963e11 | 7.03687e13 | −1.02521e16 | −2.27300e18 | 1.08843e20 | −5.90296e20 | 4.68319e22 | 8.60007e22 |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(2\) | \(1\) |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{3}^{2} - 122289844824 T_{3} - \)\(40\!\cdots\!56\)\( \) acting on \(S_{48}^{\mathrm{new}}(\Gamma_0(2))\).