Properties

Label 1035.2.i.d
Level $1035$
Weight $2$
Character orbit 1035.i
Analytic conductor $8.265$
Analytic rank $0$
Dimension $38$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1035,2,Mod(346,1035)] 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("1035.346"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1035, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1035.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [38,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.26451660920\)
Analytic rank: \(0\)
Dimension: \(38\)
Relative dimension: \(19\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 38 q + 6 q^{2} - q^{3} - 16 q^{4} - 19 q^{5} + 8 q^{6} + 5 q^{7} - 24 q^{8} + q^{9} - 12 q^{10} + 8 q^{11} - 17 q^{12} + 3 q^{14} - q^{15} - 14 q^{16} - 12 q^{17} + 27 q^{18} - 32 q^{19} - 16 q^{20}+ \cdots + 49 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
346.1 −1.22194 − 2.11647i −1.72777 − 0.121699i −1.98630 + 3.44037i −0.500000 + 0.866025i 1.85367 + 3.80548i −0.0264516 − 0.0458156i 4.82080 2.97038 + 0.420535i 2.44389
346.2 −1.12012 − 1.94010i 0.182608 + 1.72240i −1.50933 + 2.61423i −0.500000 + 0.866025i 3.13708 − 2.28357i 0.636131 + 1.10181i 2.28202 −2.93331 + 0.629048i 2.24024
346.3 −0.928800 − 1.60873i 1.53847 + 0.795686i −0.725337 + 1.25632i −0.500000 + 0.866025i −0.148885 − 3.21401i 1.24412 + 2.15489i −1.02043 1.73377 + 2.44828i 1.85760
346.4 −0.760054 − 1.31645i −1.12131 + 1.32010i −0.155363 + 0.269097i −0.500000 + 0.866025i 2.59010 + 0.472808i 0.661609 + 1.14594i −2.56788 −0.485317 − 2.96048i 1.52011
346.5 −0.733626 − 1.27068i −1.25324 − 1.19557i −0.0764128 + 0.132351i −0.500000 + 0.866025i −0.599769 + 2.46957i −1.72962 − 2.99580i −2.71027 0.141235 + 2.99667i 1.46725
346.6 −0.386840 − 0.670026i 1.19076 − 1.25781i 0.700710 − 1.21366i −0.500000 + 0.866025i −1.30340 − 0.311268i −0.669566 − 1.15972i −2.63161 −0.164187 − 2.99550i 0.773680
346.7 −0.353256 − 0.611858i −0.699962 − 1.58431i 0.750420 − 1.29977i −0.500000 + 0.866025i −0.722109 + 0.987946i 1.16178 + 2.01225i −2.47339 −2.02011 + 2.21792i 0.706512
346.8 0.0141539 + 0.0245153i −1.72519 + 0.153994i 0.999599 − 1.73136i −0.500000 + 0.866025i −0.0281934 − 0.0401139i 2.35337 + 4.07616i 0.113208 2.95257 − 0.531338i −0.0283078
346.9 0.0953508 + 0.165152i 0.802881 − 1.53473i 0.981816 − 1.70056i −0.500000 + 0.866025i 0.330019 − 0.0137396i −0.683377 − 1.18364i 0.755871 −1.71076 − 2.46440i −0.190702
346.10 0.246856 + 0.427567i 1.23350 + 1.21593i 0.878125 − 1.52096i −0.500000 + 0.866025i −0.215394 + 0.827562i −1.94772 − 3.37355i 1.85450 0.0430370 + 2.99969i −0.493711
346.11 0.290501 + 0.503162i 1.61505 + 0.625801i 0.831219 − 1.43971i −0.500000 + 0.866025i 0.154293 + 0.994425i 0.689676 + 1.19455i 2.12788 2.21675 + 2.02139i −0.581001
346.12 0.571004 + 0.989008i −0.433313 − 1.67697i 0.347908 − 0.602595i −0.500000 + 0.866025i 1.41112 − 1.38611i 0.958980 + 1.66100i 3.07865 −2.62448 + 1.45331i −1.14201
346.13 0.638639 + 1.10615i −1.17310 + 1.27430i 0.184281 − 0.319184i −0.500000 + 0.866025i −2.15876 − 0.483809i −1.95647 − 3.38870i 3.02531 −0.247685 − 2.98976i −1.27728
346.14 0.869486 + 1.50599i 1.73027 + 0.0786050i −0.512010 + 0.886828i −0.500000 + 0.866025i 1.38606 + 2.67412i 1.02751 + 1.77970i 1.69720 2.98764 + 0.272015i −1.73897
346.15 0.886780 + 1.53595i −1.73187 + 0.0251452i −0.572756 + 0.992043i −0.500000 + 0.866025i −1.57441 − 2.63776i −0.427894 − 0.741134i 1.51548 2.99874 − 0.0870962i −1.77356
346.16 1.00453 + 1.73991i −0.701812 + 1.58350i −1.01818 + 1.76354i −0.500000 + 0.866025i −3.46013 + 0.369591i 2.12196 + 3.67533i −0.0730534 −2.01492 − 2.22263i −2.00907
346.17 1.17596 + 2.03683i 1.63145 − 0.581692i −1.76578 + 3.05841i −0.500000 + 0.866025i 3.10333 + 2.63894i −0.526587 − 0.912075i −3.60209 2.32327 − 1.89801i −2.35193
346.18 1.33917 + 2.31952i −0.208460 + 1.71946i −2.58678 + 4.48043i −0.500000 + 0.866025i −4.26749 + 1.81913i 0.282442 + 0.489204i −8.49990 −2.91309 − 0.716878i −2.67835
346.19 1.37220 + 2.37671i 0.351052 − 1.69610i −2.76584 + 4.79057i −0.500000 + 0.866025i 4.51286 − 1.49303i −0.669888 − 1.16028i −9.69231 −2.75352 − 1.19084i −2.74439
691.1 −1.22194 + 2.11647i −1.72777 + 0.121699i −1.98630 − 3.44037i −0.500000 − 0.866025i 1.85367 − 3.80548i −0.0264516 + 0.0458156i 4.82080 2.97038 − 0.420535i 2.44389
See all 38 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 346.19
Significant digits:
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1035.2.i.d ✓ 38
9.c even 3 1 inner 1035.2.i.d ✓ 38
9.c even 3 1 9315.2.a.bi 19
9.d odd 6 1 9315.2.a.bj 19
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1035.2.i.d ✓ 38 1.a even 1 1 trivial
1035.2.i.d ✓ 38 9.c even 3 1 inner
9315.2.a.bi 19 9.c even 3 1
9315.2.a.bj 19 9.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{38} - 6 T_{2}^{37} + 45 T_{2}^{36} - 174 T_{2}^{35} + 826 T_{2}^{34} - 2588 T_{2}^{33} + 9655 T_{2}^{32} + \cdots + 9 \) acting on \(S_{2}^{\mathrm{new}}(1035, [\chi])\). Copy content Toggle raw display