Newspace parameters
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(59\) |
Twist minimal: | yes |
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 | −5.26507 | 0 | 19.7210 | 20.1774 | 0 | −13.2314 | −61.7120 | 0 | −106.236 | ||||||||||||||||||
1.2 | −5.24697 | 0 | 19.5307 | 10.0958 | 0 | 0.804440 | −60.5014 | 0 | −52.9726 | ||||||||||||||||||
1.3 | −5.15423 | 0 | 18.5661 | 1.27174 | 0 | −23.0732 | −54.4599 | 0 | −6.55481 | ||||||||||||||||||
1.4 | −5.11618 | 0 | 18.1753 | 6.15957 | 0 | 24.2123 | −52.0584 | 0 | −31.5134 | ||||||||||||||||||
1.5 | −5.09369 | 0 | 17.9457 | −15.2658 | 0 | −21.0984 | −50.6602 | 0 | 77.7594 | ||||||||||||||||||
1.6 | −4.50896 | 0 | 12.3307 | −9.52144 | 0 | −13.3640 | −19.5269 | 0 | 42.9318 | ||||||||||||||||||
1.7 | −4.45221 | 0 | 11.8222 | 12.0796 | 0 | −15.4984 | −17.0170 | 0 | −53.7808 | ||||||||||||||||||
1.8 | −4.45149 | 0 | 11.8157 | 14.0297 | 0 | 23.7055 | −16.9858 | 0 | −62.4530 | ||||||||||||||||||
1.9 | −4.40394 | 0 | 11.3946 | 1.03938 | 0 | 0.641944 | −14.9498 | 0 | −4.57738 | ||||||||||||||||||
1.10 | −4.10283 | 0 | 8.83322 | −7.42154 | 0 | 5.67497 | −3.41855 | 0 | 30.4493 | ||||||||||||||||||
1.11 | −3.99709 | 0 | 7.97675 | −4.04840 | 0 | −1.10463 | 0.0929295 | 0 | 16.1818 | ||||||||||||||||||
1.12 | −3.78499 | 0 | 6.32612 | −5.39134 | 0 | 9.96233 | 6.33562 | 0 | 20.4061 | ||||||||||||||||||
1.13 | −3.13470 | 0 | 1.82636 | −4.91209 | 0 | 36.3874 | 19.3525 | 0 | 15.3979 | ||||||||||||||||||
1.14 | −3.10672 | 0 | 1.65170 | −17.8784 | 0 | 0.745718 | 19.7224 | 0 | 55.5430 | ||||||||||||||||||
1.15 | −2.96448 | 0 | 0.788155 | 20.3046 | 0 | −25.7042 | 21.3794 | 0 | −60.1925 | ||||||||||||||||||
1.16 | −2.96328 | 0 | 0.781040 | 9.17370 | 0 | 2.35613 | 21.3918 | 0 | −27.1843 | ||||||||||||||||||
1.17 | −2.95118 | 0 | 0.709472 | −16.6350 | 0 | −30.2397 | 21.5157 | 0 | 49.0928 | ||||||||||||||||||
1.18 | −2.78319 | 0 | −0.253830 | 19.2360 | 0 | 27.5534 | 22.9720 | 0 | −53.5375 | ||||||||||||||||||
1.19 | −2.12161 | 0 | −3.49876 | 4.52878 | 0 | 14.7886 | 24.3959 | 0 | −9.60831 | ||||||||||||||||||
1.20 | −1.92673 | 0 | −4.28770 | −4.54299 | 0 | −14.1149 | 23.6751 | 0 | 8.75313 | ||||||||||||||||||
See all 59 embeddings |
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(3\) | \(1\) |
\(239\) | \(1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 2151.4.a.h | yes | 59 |
3.b | odd | 2 | 1 | 2151.4.a.g | ✓ | 59 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2151.4.a.g | ✓ | 59 | 3.b | odd | 2 | 1 | |
2151.4.a.h | yes | 59 | 1.a | even | 1 | 1 | trivial |