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: | \(1\) |
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 | −5.54707 | 0 | 22.7699 | −11.8059 | 0 | −16.2858 | −81.9299 | 0 | 65.4880 | ||||||||||||||||||
1.2 | −5.50845 | 0 | 22.3430 | 10.5610 | 0 | 7.83920 | −79.0077 | 0 | −58.1747 | ||||||||||||||||||
1.3 | −5.43867 | 0 | 21.5792 | −5.07597 | 0 | 21.4842 | −73.8527 | 0 | 27.6066 | ||||||||||||||||||
1.4 | −5.06856 | 0 | 17.6903 | 14.8628 | 0 | −19.8824 | −49.1160 | 0 | −75.3330 | ||||||||||||||||||
1.5 | −4.88066 | 0 | 15.8208 | −22.1582 | 0 | 19.1765 | −38.1708 | 0 | 108.146 | ||||||||||||||||||
1.6 | −4.81368 | 0 | 15.1715 | −10.3877 | 0 | 20.9834 | −34.5214 | 0 | 50.0029 | ||||||||||||||||||
1.7 | −4.79889 | 0 | 15.0293 | −17.2694 | 0 | 7.94711 | −33.7329 | 0 | 82.8740 | ||||||||||||||||||
1.8 | −4.59357 | 0 | 13.1009 | 7.15514 | 0 | 33.8683 | −23.4314 | 0 | −32.8677 | ||||||||||||||||||
1.9 | −4.52883 | 0 | 12.5103 | −9.53238 | 0 | −26.9020 | −20.4262 | 0 | 43.1705 | ||||||||||||||||||
1.10 | −4.39292 | 0 | 11.2977 | 17.5164 | 0 | 15.6908 | −14.4866 | 0 | −76.9482 | ||||||||||||||||||
1.11 | −4.26856 | 0 | 10.2206 | 4.08830 | 0 | −28.0668 | −9.47876 | 0 | −17.4512 | ||||||||||||||||||
1.12 | −3.66557 | 0 | 5.43642 | 19.0359 | 0 | −9.80549 | 9.39697 | 0 | −69.7775 | ||||||||||||||||||
1.13 | −3.55261 | 0 | 4.62104 | −5.70782 | 0 | 19.6278 | 12.0041 | 0 | 20.2777 | ||||||||||||||||||
1.14 | −3.36448 | 0 | 3.31971 | −9.29992 | 0 | 3.75868 | 15.7467 | 0 | 31.2894 | ||||||||||||||||||
1.15 | −3.23820 | 0 | 2.48591 | −18.9858 | 0 | −17.9377 | 17.8557 | 0 | 61.4797 | ||||||||||||||||||
1.16 | −3.14305 | 0 | 1.87878 | 8.40099 | 0 | 6.53557 | 19.2393 | 0 | −26.4048 | ||||||||||||||||||
1.17 | −3.12258 | 0 | 1.75053 | 10.0516 | 0 | −27.9204 | 19.5145 | 0 | −31.3869 | ||||||||||||||||||
1.18 | −2.94849 | 0 | 0.693582 | 3.01150 | 0 | −30.9852 | 21.5429 | 0 | −8.87936 | ||||||||||||||||||
1.19 | −2.83641 | 0 | 0.0452483 | 6.73903 | 0 | 0.810661 | 22.5630 | 0 | −19.1147 | ||||||||||||||||||
1.20 | −2.81951 | 0 | −0.0503577 | −16.9496 | 0 | 31.0725 | 22.6981 | 0 | 47.7895 | ||||||||||||||||||
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.g | ✓ | 59 |
3.b | odd | 2 | 1 | 2151.4.a.h | yes | 59 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
2151.4.a.g | ✓ | 59 | 1.a | even | 1 | 1 | trivial |
2151.4.a.h | yes | 59 | 3.b | odd | 2 | 1 |