↑

Properties

Label 889.2.f.c
Level $889$
Weight $2$
Character orbit 889.f
Analytic conductor $7.099$
Analytic rank $0$
Dimension $76$
Inner twists $2$

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] = [889,2,Mod(128,889)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("889.128"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(889, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 889 = 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 889.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.09870073969\)
Analytic rank: \(0\)
Dimension: \(76\)
Relative dimension: \(38\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 76 q + 2 q^{2} - 11 q^{3} - 38 q^{4} - 16 q^{5} + 22 q^{6} + 3 q^{7} - 47 q^{9} - 12 q^{10} + 2 q^{11} - 30 q^{12} + 42 q^{13} - 2 q^{14} + 14 q^{15} - 46 q^{16} - 58 q^{17} + 13 q^{18} - 17 q^{19} + 88 q^{20}+ \cdots + 32 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
128.1 −1.39191 + 2.41086i −0.640277 − 1.10899i −2.87482 − 4.97933i −0.367645 + 0.636780i 3.56483 2.64566 − 0.0217269i 10.4383 0.680090 − 1.17795i −1.02346 − 1.77268i
128.2 −1.28080 + 2.21842i 0.273672 + 0.474014i −2.28092 − 3.95066i −1.09635 + 1.89893i −1.40208 −2.36338 − 1.18930i 6.56242 1.35021 − 2.33863i −2.80841 − 4.86431i
128.3 −1.23110 + 2.13233i −1.14184 − 1.97773i −2.03121 − 3.51815i −1.58906 + 2.75234i 5.62287 −1.40724 − 2.24046i 5.07807 −1.10760 + 1.91842i −3.91259 − 6.77680i
128.4 −1.20231 + 2.08246i −1.27729 − 2.21232i −1.89109 − 3.27546i −1.15195 + 1.99523i 6.14276 −0.328118 + 2.62533i 4.28546 −1.76291 + 3.05346i −2.76999 − 4.79776i
128.5 −1.10624 + 1.91606i 1.41629 + 2.45309i −1.44753 − 2.50720i −2.05646 + 3.56190i −6.26703 1.74804 + 1.98604i 1.98031 −2.51176 + 4.35049i −4.54988 − 7.88063i
128.6 −1.07997 + 1.87056i −1.54134 − 2.66967i −1.33266 − 2.30824i 1.38242 − 2.39442i 6.65837 −2.64073 + 0.162968i 1.43706 −3.25143 + 5.63164i 2.98594 + 5.17180i
128.7 −1.05675 + 1.83034i −0.749904 − 1.29887i −1.23343 − 2.13637i 1.90799 − 3.30473i 3.16984 2.62812 − 0.304958i 0.986711 0.375288 − 0.650017i 4.03252 + 6.98454i
128.8 −1.03772 + 1.79738i 0.602800 + 1.04408i −1.15372 − 1.99830i 0.484747 − 0.839607i −2.50215 −0.477806 − 2.60225i 0.638058 0.773264 − 1.33933i 1.00606 + 1.74255i
128.9 −0.821718 + 1.42326i −0.0910116 − 0.157637i −0.350440 − 0.606979i −1.56327 + 2.70766i 0.299143 2.48951 + 0.895730i −2.13502 1.48343 − 2.56938i −2.56913 − 4.44986i
128.10 −0.772637 + 1.33825i 0.726509 + 1.25835i −0.193937 − 0.335908i 0.318832 − 0.552233i −2.24531 1.25512 − 2.32909i −2.49118 0.444369 − 0.769670i 0.492683 + 0.853352i
128.11 −0.696843 + 1.20697i −1.44710 − 2.50645i 0.0288204 + 0.0499184i −1.16345 + 2.01515i 4.03360 2.41679 − 1.07664i −2.86770 −2.68819 + 4.65608i −1.62148 − 2.80849i
128.12 −0.574585 + 0.995211i −0.756468 − 1.31024i 0.339704 + 0.588384i 0.0918047 − 0.159010i 1.73862 −2.24835 − 1.39460i −3.07910 0.355514 − 0.615768i 0.105499 + 0.182730i
128.13 −0.522750 + 0.905429i −0.0163100 − 0.0282498i 0.453465 + 0.785424i 1.25204 − 2.16859i 0.0341043 2.35840 − 1.19914i −3.03919 1.49947 − 2.59715i 1.30900 + 2.26726i
128.14 −0.377450 + 0.653763i 1.60447 + 2.77903i 0.715063 + 1.23852i 0.834745 − 1.44582i −2.42244 −2.43055 + 1.04518i −2.58940 −3.64868 + 6.31969i 0.630150 + 1.09145i
128.15 −0.372933 + 0.645939i −1.16060 − 2.01022i 0.721842 + 1.25027i −2.20437 + 3.81808i 1.73131 −1.27971 + 2.31567i −2.56853 −1.19400 + 2.06807i −1.64416 − 2.84778i
128.16 −0.249488 + 0.432126i 1.03209 + 1.78764i 0.875512 + 1.51643i −0.148376 + 0.256995i −1.02998 −1.94788 + 1.79046i −1.87167 −0.630427 + 1.09193i −0.0740361 − 0.128234i
128.17 −0.109772 + 0.190131i 0.116430 + 0.201662i 0.975900 + 1.69031i −0.316233 + 0.547731i −0.0511230 −2.64381 + 0.101345i −0.867596 1.47289 − 2.55112i −0.0694272 − 0.120251i
128.18 −0.0444553 + 0.0769989i −0.252730 − 0.437742i 0.996047 + 1.72520i −1.10783 + 1.91882i 0.0449408 1.44219 − 2.21813i −0.354940 1.37225 − 2.37682i −0.0984981 − 0.170604i
128.19 0.0209719 − 0.0363243i 0.961799 + 1.66588i 0.999120 + 1.73053i 0.410006 − 0.710151i 0.0806829 −0.491457 − 2.59971i 0.167701 −0.350115 + 0.606416i −0.0171972 − 0.0297864i
128.20 0.247141 − 0.428060i −0.842389 − 1.45906i 0.877843 + 1.52047i 0.338209 − 0.585795i −0.832754 2.64457 − 0.0789416i 1.85636 0.0807616 − 0.139883i −0.167170 − 0.289548i
See all 76 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 128.38
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 889.2.f.c ✓ 76
7.c even 3 1 inner 889.2.f.c ✓ 76
7.c even 3 1 6223.2.a.p 38
7.d odd 6 1 6223.2.a.o 38
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
889.2.f.c ✓ 76 1.a even 1 1 trivial
889.2.f.c ✓ 76 7.c even 3 1 inner
6223.2.a.o 38 7.d odd 6 1
6223.2.a.p 38 7.c even 3 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{76} - 2 T_{2}^{75} + 59 T_{2}^{74} - 110 T_{2}^{73} + 1873 T_{2}^{72} - 3312 T_{2}^{71} + \cdots + 45369 \) acting on \(S_{2}^{\mathrm{new}}(889, [\chi])\). Copy content Toggle raw display