Newspace parameters
Level: | \( N \) | = | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 2005.a (trivial) |
Newform invariants
Self dual: | Yes |
Analytic conductor: | \(16.0100056053\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace 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 | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 | −2.69709 | −2.81518 | 5.27428 | −1.00000 | 7.59279 | −1.69501 | −8.83103 | 4.92525 | 2.69709 | ||||||||||||||||||
1.2 | −2.59156 | 0.254340 | 4.71619 | −1.00000 | −0.659137 | −3.82594 | −7.03917 | −2.93531 | 2.59156 | ||||||||||||||||||
1.3 | −2.45894 | 0.456001 | 4.04640 | −1.00000 | −1.12128 | 2.81754 | −5.03197 | −2.79206 | 2.45894 | ||||||||||||||||||
1.4 | −2.34377 | 3.11940 | 3.49326 | −1.00000 | −7.31116 | −3.06432 | −3.49986 | 6.73066 | 2.34377 | ||||||||||||||||||
1.5 | −2.29904 | −2.37846 | 3.28561 | −1.00000 | 5.46819 | −1.14540 | −2.95567 | 2.65708 | 2.29904 | ||||||||||||||||||
1.6 | −2.05755 | 2.25661 | 2.23350 | −1.00000 | −4.64308 | 1.74407 | −0.480444 | 2.09227 | 2.05755 | ||||||||||||||||||
1.7 | −1.89780 | 0.675950 | 1.60165 | −1.00000 | −1.28282 | −2.83198 | 0.755984 | −2.54309 | 1.89780 | ||||||||||||||||||
1.8 | −1.67554 | −1.95480 | 0.807444 | −1.00000 | 3.27536 | 1.89440 | 1.99818 | 0.821260 | 1.67554 | ||||||||||||||||||
1.9 | −1.33194 | −3.14709 | −0.225946 | −1.00000 | 4.19172 | −4.67738 | 2.96482 | 6.90415 | 1.33194 | ||||||||||||||||||
1.10 | −1.31166 | 2.95262 | −0.279548 | −1.00000 | −3.87283 | 1.12020 | 2.98999 | 5.71797 | 1.31166 | ||||||||||||||||||
1.11 | −1.26616 | −0.778484 | −0.396848 | −1.00000 | 0.985683 | −1.29163 | 3.03478 | −2.39396 | 1.26616 | ||||||||||||||||||
1.12 | −1.00292 | −0.400121 | −0.994154 | −1.00000 | 0.401289 | 0.439579 | 3.00289 | −2.83990 | 1.00292 | ||||||||||||||||||
1.13 | −0.973849 | 1.32303 | −1.05162 | −1.00000 | −1.28843 | 3.84920 | 2.97182 | −1.24959 | 0.973849 | ||||||||||||||||||
1.14 | −0.667454 | −3.21238 | −1.55450 | −1.00000 | 2.14411 | 2.82900 | 2.37247 | 7.31937 | 0.667454 | ||||||||||||||||||
1.15 | −0.481240 | 0.287327 | −1.76841 | −1.00000 | −0.138273 | −4.64922 | 1.81351 | −2.91744 | 0.481240 | ||||||||||||||||||
1.16 | −0.272348 | 1.38053 | −1.92583 | −1.00000 | −0.375985 | −0.00887442 | 1.06919 | −1.09413 | 0.272348 | ||||||||||||||||||
1.17 | −0.141163 | 1.61581 | −1.98007 | −1.00000 | −0.228092 | −0.325783 | 0.561837 | −0.389145 | 0.141163 | ||||||||||||||||||
1.18 | 0.0750780 | 3.37448 | −1.99436 | −1.00000 | 0.253350 | 1.31500 | −0.299889 | 8.38713 | −0.0750780 | ||||||||||||||||||
1.19 | 0.210270 | −2.86952 | −1.95579 | −1.00000 | −0.603374 | 0.843239 | −0.831782 | 5.23416 | −0.210270 | ||||||||||||||||||
1.20 | 0.287516 | 0.183703 | −1.91733 | −1.00000 | 0.0528174 | −5.18007 | −1.12630 | −2.96625 | −0.287516 | ||||||||||||||||||
See all 37 embeddings |
Inner twists
This newform does not have CM; other inner twists have not been computed.
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(1\) |
\(401\) | \(-1\) |
Hecke kernels
This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\):
\(T_{2}^{37} - \cdots\) |
\(T_{11}^{37} - \cdots\) |