↑

Properties

Label 855.2.dl.b
Level $855$
Weight $2$
Character orbit 855.dl
Analytic conductor $6.827$
Analytic rank $0$
Dimension $240$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.dl (of order \(36\), degree \(12\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [240,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(20\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 285)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 240 q - 12 q^{7} - 36 q^{16} - 120 q^{20} + 24 q^{22} - 24 q^{23} - 24 q^{25} + 24 q^{26} - 72 q^{28} + 12 q^{32} + 132 q^{38} - 132 q^{40} + 72 q^{41} - 108 q^{43} - 24 q^{47} - 36 q^{53} - 144 q^{58}+ \cdots - 192 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
127.1 −0.245186 + 2.80249i 0 −5.82423 − 1.02697i 1.59490 + 1.56726i 0 3.36189 − 0.900815i 2.84987 − 10.6359i 0 −4.78327 + 4.08543i
127.2 −0.221131 + 2.52754i 0 −4.36997 − 0.770543i 1.88209 − 1.20736i 0 −4.24987 + 1.13875i 1.60057 − 5.97340i 0 2.63547 + 5.02406i
127.3 −0.211271 + 2.41484i 0 −3.81721 − 0.673077i −2.02651 − 0.945118i 0 3.31457 − 0.888135i 1.17705 − 4.39281i 0 2.71045 − 4.69403i
127.4 −0.174085 + 1.98980i 0 −1.95939 − 0.345493i −2.20715 + 0.358426i 0 −0.645153 + 0.172868i −0.00536850 + 0.0200355i 0 −0.328963 − 4.45420i
127.5 −0.139189 + 1.59093i 0 −0.542082 − 0.0955836i 1.29857 + 1.82036i 0 −3.32108 + 0.889881i −0.599155 + 2.23608i 0 −3.07683 + 1.81256i
127.6 −0.123273 + 1.40901i 0 −0.000501844 0 8.84886e-5i 0.196721 + 2.22740i 0 −0.304645 + 0.0816294i −0.731958 + 2.73170i 0 −3.16268 + 0.00260585i
127.7 −0.0645910 + 0.738279i 0 1.42873 + 0.251924i −2.03490 + 0.926932i 0 −0.698543 + 0.187174i −0.661894 + 2.47022i 0 −0.552898 − 1.56219i
127.8 −0.0606620 + 0.693370i 0 1.49253 + 0.263174i −1.87105 − 1.22441i 0 −0.186172 + 0.0498847i −0.633303 + 2.36352i 0 0.962473 − 1.22305i
127.9 −0.0411489 + 0.470334i 0 1.75009 + 0.308589i 1.85799 − 1.24413i 0 3.79411 − 1.01663i −0.461547 + 1.72252i 0 0.508705 + 0.925072i
127.10 0.0109248 − 0.124871i 0 1.95414 + 0.344568i 1.90054 − 1.17811i 0 −0.778755 + 0.208667i 0.129260 − 0.482404i 0 −0.126349 − 0.250192i
127.11 0.0357601 − 0.408739i 0 1.80383 + 0.318063i −0.989844 + 2.00505i 0 1.11081 − 0.297640i 0.406897 − 1.51856i 0 0.784144 + 0.476289i
127.12 0.0377436 − 0.431412i 0 1.78492 + 0.314730i −1.01360 − 1.99314i 0 3.12027 − 0.836073i 0.427316 − 1.59476i 0 −0.898121 + 0.362052i
127.13 0.0705291 − 0.806152i 0 1.32471 + 0.233582i 0.792231 − 2.09102i 0 −4.52694 + 1.21299i 0.700622 − 2.61476i 0 −1.62980 − 0.786136i
127.14 0.103868 − 1.18722i 0 0.570922 + 0.100669i 0.683867 + 2.12893i 0 3.81081 − 1.02110i 0.795712 − 2.96964i 0 2.59853 − 0.590771i
127.15 0.104634 − 1.19597i 0 0.550219 + 0.0970185i −2.17241 + 0.529758i 0 −4.48710 + 1.20231i 0.795047 − 2.96716i 0 0.406267 + 2.65357i
127.16 0.154999 − 1.77165i 0 −1.14509 − 0.201911i 1.97375 + 1.05086i 0 −3.11238 + 0.833960i 0.385372 − 1.43823i 0 2.16768 − 3.33391i
127.17 0.174703 − 1.99687i 0 −1.98735 − 0.350423i 0.0877739 − 2.23434i 0 3.92524 − 1.05176i −0.00934001 + 0.0348574i 0 −4.44636 − 0.565620i
127.18 0.191383 − 2.18751i 0 −2.77898 − 0.490009i 1.60864 + 1.55315i 0 −3.10944 + 0.833171i −0.467084 + 1.74318i 0 3.70541 − 3.22167i
127.19 0.194011 − 2.21755i 0 −2.91027 − 0.513160i −0.750110 + 2.10650i 0 0.717202 − 0.192174i −0.550308 + 2.05378i 0 4.52574 + 2.07209i
127.20 0.201982 − 2.30867i 0 −3.31953 − 0.585323i −0.464206 − 2.18735i 0 −0.466867 + 0.125097i −0.822183 + 3.06843i 0 −5.14363 + 0.629891i
See next 80 embeddings (of 240 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 127.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.c odd 4 1 inner
19.f odd 18 1 inner
95.r even 36 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 855.2.dl.b 240
3.b odd 2 1 285.2.bh.a ✓ 240
5.c odd 4 1 inner 855.2.dl.b 240
15.e even 4 1 285.2.bh.a ✓ 240
19.f odd 18 1 inner 855.2.dl.b 240
57.j even 18 1 285.2.bh.a ✓ 240
95.r even 36 1 inner 855.2.dl.b 240
285.bj odd 36 1 285.2.bh.a ✓ 240
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
285.2.bh.a ✓ 240 3.b odd 2 1
285.2.bh.a ✓ 240 15.e even 4 1
285.2.bh.a ✓ 240 57.j even 18 1
285.2.bh.a ✓ 240 285.bj odd 36 1
855.2.dl.b 240 1.a even 1 1 trivial
855.2.dl.b 240 5.c odd 4 1 inner
855.2.dl.b 240 19.f odd 18 1 inner
855.2.dl.b 240 95.r even 36 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{240} + 45 T_{2}^{236} - 60 T_{2}^{235} - 984 T_{2}^{233} + 1206 T_{2}^{232} + \cdots + 15\!\cdots\!56 \) acting on \(S_{2}^{\mathrm{new}}(855, [\chi])\). Copy content Toggle raw display