Properties

Label 805.2.i.d
Level $805$
Weight $2$
Character orbit 805.i
Analytic conductor $6.428$
Analytic rank $0$
Dimension $26$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [805,2,Mod(116,805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(805, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.116");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.42795736271\)
Analytic rank: \(0\)
Dimension: \(26\)
Relative dimension: \(13\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 5 q^{2} + 2 q^{3} - 13 q^{4} - 13 q^{5} - 8 q^{6} - 30 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q + 5 q^{2} + 2 q^{3} - 13 q^{4} - 13 q^{5} - 8 q^{6} - 30 q^{8} - 5 q^{9} + 5 q^{10} + 17 q^{11} - 6 q^{12} + 2 q^{13} + 11 q^{14} - 4 q^{15} - 21 q^{16} - 2 q^{17} + 25 q^{18} + 13 q^{19} + 26 q^{20} + 5 q^{21} + 6 q^{22} - 13 q^{23} + 20 q^{24} - 13 q^{25} + 2 q^{26} - 10 q^{27} + 23 q^{28} - 52 q^{29} + 4 q^{30} - 8 q^{31} + 40 q^{32} + 6 q^{33} - 84 q^{34} + 3 q^{35} + 34 q^{36} + 29 q^{37} - 40 q^{38} + 20 q^{39} + 15 q^{40} - 56 q^{41} - 18 q^{42} - 20 q^{43} + 31 q^{44} - 5 q^{45} + 5 q^{46} - q^{47} + 16 q^{48} - 4 q^{49} - 10 q^{50} + 3 q^{51} - 27 q^{52} + 43 q^{53} + 24 q^{54} - 34 q^{55} - 24 q^{56} + 4 q^{57} - 24 q^{58} + q^{59} - 6 q^{60} + 30 q^{61} - 4 q^{62} + 8 q^{63} + 70 q^{64} - q^{65} - 71 q^{66} + 21 q^{67} - 11 q^{68} - 4 q^{69} + 5 q^{70} + 47 q^{72} - 5 q^{73} + 10 q^{74} + 2 q^{75} - 174 q^{76} - 2 q^{77} + 58 q^{78} + 36 q^{79} - 21 q^{80} + 35 q^{81} - 8 q^{82} - 22 q^{84} + 4 q^{85} + 20 q^{86} - 6 q^{87} + 24 q^{88} + 10 q^{89} - 50 q^{90} + 36 q^{91} + 26 q^{92} + 15 q^{93} - 38 q^{94} + 13 q^{95} + 31 q^{96} - 16 q^{97} + 41 q^{98} - 18 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
116.1 −1.21151 2.09840i 0.545639 0.945074i −1.93551 + 3.35240i −0.500000 0.866025i −2.64419 −1.33047 + 2.28689i 4.53352 0.904556 + 1.56674i −1.21151 + 2.09840i
116.2 −0.930075 1.61094i −0.647848 + 1.12211i −0.730080 + 1.26454i −0.500000 0.866025i 2.41019 −0.321023 2.62620i −1.00418 0.660585 + 1.14417i −0.930075 + 1.61094i
116.3 −0.808540 1.40043i 0.950902 1.64701i −0.307475 + 0.532562i −0.500000 0.866025i −3.07537 −1.85596 1.88558i −2.23974 −0.308430 0.534217i −0.808540 + 1.40043i
116.4 −0.403896 0.699568i −0.435726 + 0.754699i 0.673736 1.16695i −0.500000 0.866025i 0.703952 2.64245 + 0.132096i −2.70406 1.12029 + 1.94039i −0.403896 + 0.699568i
116.5 −0.315573 0.546589i −0.746000 + 1.29211i 0.800827 1.38707i −0.500000 0.866025i 0.941671 −1.51243 + 2.17084i −2.27317 0.386967 + 0.670247i −0.315573 + 0.546589i
116.6 0.0122895 + 0.0212861i 1.20990 2.09561i 0.999698 1.73153i −0.500000 0.866025i 0.0594766 −0.797907 + 2.52257i 0.0983013 −1.42773 2.47291i 0.0122895 0.0212861i
116.7 0.331631 + 0.574401i 0.0704605 0.122041i 0.780042 1.35107i −0.500000 0.866025i 0.0934675 2.61178 0.422600i 2.36127 1.49007 + 2.58088i 0.331631 0.574401i
116.8 0.407561 + 0.705916i 1.49351 2.58683i 0.667789 1.15664i −0.500000 0.866025i 2.43478 2.16383 + 1.52245i 2.71890 −2.96114 5.12884i 0.407561 0.705916i
116.9 0.715027 + 1.23846i −0.647175 + 1.12094i −0.0225278 + 0.0390193i −0.500000 0.866025i −1.85099 −2.26678 + 1.36444i 2.79568 0.662330 + 1.14719i 0.715027 1.23846i
116.10 0.818862 + 1.41831i −0.993060 + 1.72003i −0.341070 + 0.590750i −0.500000 0.866025i −3.25272 0.0983737 2.64392i 2.15829 −0.472336 0.818110i 0.818862 1.41831i
116.11 1.22768 + 2.12640i 0.865673 1.49939i −2.01438 + 3.48901i −0.500000 0.866025i 4.25107 0.636983 2.56793i −4.98133 0.00121936 + 0.00211200i 1.22768 2.12640i
116.12 1.26952 + 2.19888i 0.797397 1.38113i −2.22339 + 3.85102i −0.500000 0.866025i 4.04926 −2.50585 + 0.848950i −6.21247 0.228316 + 0.395455i 1.26952 2.19888i
116.13 1.38702 + 2.40239i −1.46368 + 2.53516i −2.84766 + 4.93230i −0.500000 0.866025i −8.12060 2.43700 + 1.03006i −10.2510 −2.78469 4.82323i 1.38702 2.40239i
576.1 −1.21151 + 2.09840i 0.545639 + 0.945074i −1.93551 3.35240i −0.500000 + 0.866025i −2.64419 −1.33047 2.28689i 4.53352 0.904556 1.56674i −1.21151 2.09840i
576.2 −0.930075 + 1.61094i −0.647848 1.12211i −0.730080 1.26454i −0.500000 + 0.866025i 2.41019 −0.321023 + 2.62620i −1.00418 0.660585 1.14417i −0.930075 1.61094i
576.3 −0.808540 + 1.40043i 0.950902 + 1.64701i −0.307475 0.532562i −0.500000 + 0.866025i −3.07537 −1.85596 + 1.88558i −2.23974 −0.308430 + 0.534217i −0.808540 1.40043i
576.4 −0.403896 + 0.699568i −0.435726 0.754699i 0.673736 + 1.16695i −0.500000 + 0.866025i 0.703952 2.64245 0.132096i −2.70406 1.12029 1.94039i −0.403896 0.699568i
576.5 −0.315573 + 0.546589i −0.746000 1.29211i 0.800827 + 1.38707i −0.500000 + 0.866025i 0.941671 −1.51243 2.17084i −2.27317 0.386967 0.670247i −0.315573 0.546589i
576.6 0.0122895 0.0212861i 1.20990 + 2.09561i 0.999698 + 1.73153i −0.500000 + 0.866025i 0.0594766 −0.797907 2.52257i 0.0983013 −1.42773 + 2.47291i 0.0122895 + 0.0212861i
576.7 0.331631 0.574401i 0.0704605 + 0.122041i 0.780042 + 1.35107i −0.500000 + 0.866025i 0.0934675 2.61178 + 0.422600i 2.36127 1.49007 2.58088i 0.331631 + 0.574401i
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 116.13
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 805.2.i.d 26
7.c even 3 1 inner 805.2.i.d 26
7.c even 3 1 5635.2.a.be 13
7.d odd 6 1 5635.2.a.bf 13
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.i.d 26 1.a even 1 1 trivial
805.2.i.d 26 7.c even 3 1 inner
5635.2.a.be 13 7.c even 3 1
5635.2.a.bf 13 7.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{26} - 5 T_{2}^{25} + 32 T_{2}^{24} - 95 T_{2}^{23} + 394 T_{2}^{22} - 942 T_{2}^{21} + 3126 T_{2}^{20} - 5999 T_{2}^{19} + 16174 T_{2}^{18} - 25410 T_{2}^{17} + 59664 T_{2}^{16} - 77081 T_{2}^{15} + 153225 T_{2}^{14} - 157790 T_{2}^{13} + \cdots + 4 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display