Newspace parameters
Level: | \( N \) | = | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | = | \( 4 \) |
Character orbit: | \([\chi]\) | = | 14.c (of order \(3\) and degree \(2\)) |
Newform invariants
Self dual: | No |
Analytic conductor: | \(0.82602674008\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-3}) \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{6}\). We also show the integral \(q\)-expansion of the trace form.
Character Values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1 + \zeta_{6}\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9.1 |
|
−1.00000 | + | 1.73205i | 2.50000 | + | 4.33013i | −2.00000 | − | 3.46410i | 4.50000 | − | 7.79423i | −10.0000 | −14.0000 | − | 12.1244i | 8.00000 | 1.00000 | − | 1.73205i | 9.00000 | + | 15.5885i | ||||||||||
11.1 | −1.00000 | − | 1.73205i | 2.50000 | − | 4.33013i | −2.00000 | + | 3.46410i | 4.50000 | + | 7.79423i | −10.0000 | −14.0000 | + | 12.1244i | 8.00000 | 1.00000 | + | 1.73205i | 9.00000 | − | 15.5885i |
Inner twists
Char. orbit | Parity | Mult. | Self Twist | Proved |
---|---|---|---|---|
1.a | Even | 1 | trivial | yes |
7.c | Even | 1 | yes |
Hecke kernels
This newform can be constructed as the kernel of the linear operator \( T_{3}^{2} - 5 T_{3} + 25 \) acting on \(S_{4}^{\mathrm{new}}(14, [\chi])\).