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Properties

Label 805.2.i.c
Level $805$
Weight $2$
Character orbit 805.i
Analytic conductor $6.428$
Analytic rank $0$
Dimension $24$
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: \(24\)
Relative dimension: \(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 7 q^{2} + 2 q^{3} - 7 q^{4} + 12 q^{5} + 3 q^{7} - 30 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 7 q^{2} + 2 q^{3} - 7 q^{4} + 12 q^{5} + 3 q^{7} - 30 q^{8} - 4 q^{9} - 7 q^{10} + 3 q^{11} + 4 q^{12} + 6 q^{13} - 13 q^{14} + 4 q^{15} - q^{16} - 4 q^{17} - 3 q^{18} - 17 q^{19} - 14 q^{20} - 19 q^{21} + 10 q^{22} + 12 q^{23} - 12 q^{24} - 12 q^{25} + 6 q^{26} + 2 q^{27} - 13 q^{28} - 50 q^{29} - 11 q^{31} + 12 q^{32} - 10 q^{33} + 12 q^{34} + 3 q^{35} - 10 q^{36} + 18 q^{37} + 6 q^{38} + 20 q^{39} - 15 q^{40} + 30 q^{41} + 58 q^{42} + 30 q^{43} + 7 q^{44} + 4 q^{45} - 7 q^{46} + 23 q^{47} - 20 q^{48} + 29 q^{49} - 14 q^{50} + 15 q^{51} - 33 q^{52} + 19 q^{53} - 12 q^{54} + 6 q^{55} + 20 q^{56} - 28 q^{57} + 12 q^{58} - 15 q^{59} - 4 q^{60} - 28 q^{61} - 8 q^{62} + 102 q^{64} + 3 q^{65} - 23 q^{66} + 14 q^{67} + 13 q^{68} + 4 q^{69} + q^{70} - 32 q^{71} + q^{72} + 19 q^{73} + 42 q^{74} + 2 q^{75} - 6 q^{76} + 38 q^{77} + 74 q^{78} - 4 q^{79} + q^{80} + 8 q^{81} + 2 q^{82} + 14 q^{83} + 66 q^{84} - 8 q^{85} + 2 q^{86} - 34 q^{87} - 24 q^{88} + 4 q^{89} - 6 q^{90} + 2 q^{91} - 14 q^{92} + 69 q^{93} - 74 q^{94} + 17 q^{95} - 9 q^{96} - 42 q^{97} - 33 q^{98} - 86 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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 −0.922830 − 1.59839i 0.165730 − 0.287053i −0.703232 + 1.21803i 0.500000 + 0.866025i −0.611764 2.52441 − 0.792066i −1.09547 1.44507 + 2.50293i 0.922830 − 1.59839i
116.2 −0.635758 − 1.10117i 1.39397 − 2.41443i 0.191622 − 0.331900i 0.500000 + 0.866025i −3.54492 −2.62097 + 0.361293i −3.03034 −2.38631 − 4.13321i 0.635758 − 1.10117i
116.3 −0.560072 − 0.970074i −1.41854 + 2.45699i 0.372638 − 0.645428i 0.500000 + 0.866025i 3.17795 2.63970 − 0.178790i −3.07511 −2.52454 − 4.37262i 0.560072 − 0.970074i
116.4 −0.280987 − 0.486684i 0.0708183 − 0.122661i 0.842093 − 1.45855i 0.500000 + 0.866025i −0.0795961 −2.43289 − 1.03974i −2.07042 1.48997 + 2.58070i 0.280987 − 0.486684i
116.5 −0.189972 − 0.329042i 0.798109 − 1.38236i 0.927821 − 1.60703i 0.500000 + 0.866025i −0.606475 2.05783 + 1.66292i −1.46493 0.226045 + 0.391522i 0.189972 − 0.329042i
116.6 0.356940 + 0.618238i −0.363936 + 0.630356i 0.745188 − 1.29070i 0.500000 + 0.866025i −0.519613 1.55377 − 2.14145i 2.49171 1.23510 + 2.13926i −0.356940 + 0.618238i
116.7 0.587188 + 1.01704i −0.929890 + 1.61062i 0.310420 − 0.537664i 0.500000 + 0.866025i −2.18408 −2.26351 + 1.36986i 3.07785 −0.229390 − 0.397315i −0.587188 + 1.01704i
116.8 0.677952 + 1.17425i 1.20421 − 2.08575i 0.0807614 − 0.139883i 0.500000 + 0.866025i 3.26558 2.53030 − 0.773031i 2.93082 −1.40023 − 2.42527i −0.677952 + 1.17425i
116.9 0.873183 + 1.51240i −0.125242 + 0.216926i −0.524896 + 0.909147i 0.500000 + 0.866025i −0.437438 −1.93664 − 1.80261i 1.65941 1.46863 + 2.54374i −0.873183 + 1.51240i
116.10 1.05319 + 1.82418i −1.18723 + 2.05634i −1.21843 + 2.11037i 0.500000 + 0.866025i −5.00153 0.0851231 + 2.64438i −0.920175 −1.31903 − 2.28463i −1.05319 + 1.82418i
116.11 1.14168 + 1.97745i 1.21263 − 2.10034i −1.60686 + 2.78316i 0.500000 + 0.866025i 5.53775 0.383330 − 2.61783i −2.77136 −1.44096 − 2.49582i −1.14168 + 1.97745i
116.12 1.39949 + 2.42398i 0.179374 − 0.310685i −2.91713 + 5.05262i 0.500000 + 0.866025i 1.00413 −1.02046 + 2.44104i −10.7320 1.43565 + 2.48662i −1.39949 + 2.42398i
576.1 −0.922830 + 1.59839i 0.165730 + 0.287053i −0.703232 − 1.21803i 0.500000 − 0.866025i −0.611764 2.52441 + 0.792066i −1.09547 1.44507 − 2.50293i 0.922830 + 1.59839i
576.2 −0.635758 + 1.10117i 1.39397 + 2.41443i 0.191622 + 0.331900i 0.500000 − 0.866025i −3.54492 −2.62097 − 0.361293i −3.03034 −2.38631 + 4.13321i 0.635758 + 1.10117i
576.3 −0.560072 + 0.970074i −1.41854 − 2.45699i 0.372638 + 0.645428i 0.500000 − 0.866025i 3.17795 2.63970 + 0.178790i −3.07511 −2.52454 + 4.37262i 0.560072 + 0.970074i
576.4 −0.280987 + 0.486684i 0.0708183 + 0.122661i 0.842093 + 1.45855i 0.500000 − 0.866025i −0.0795961 −2.43289 + 1.03974i −2.07042 1.48997 − 2.58070i 0.280987 + 0.486684i
576.5 −0.189972 + 0.329042i 0.798109 + 1.38236i 0.927821 + 1.60703i 0.500000 − 0.866025i −0.606475 2.05783 − 1.66292i −1.46493 0.226045 − 0.391522i 0.189972 + 0.329042i
576.6 0.356940 − 0.618238i −0.363936 − 0.630356i 0.745188 + 1.29070i 0.500000 − 0.866025i −0.519613 1.55377 + 2.14145i 2.49171 1.23510 − 2.13926i −0.356940 − 0.618238i
576.7 0.587188 − 1.01704i −0.929890 − 1.61062i 0.310420 + 0.537664i 0.500000 − 0.866025i −2.18408 −2.26351 − 1.36986i 3.07785 −0.229390 + 0.397315i −0.587188 − 1.01704i
576.8 0.677952 − 1.17425i 1.20421 + 2.08575i 0.0807614 + 0.139883i 0.500000 − 0.866025i 3.26558 2.53030 + 0.773031i 2.93082 −1.40023 + 2.42527i −0.677952 − 1.17425i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 116.12
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.c ✓ 24
7.c even 3 1 inner 805.2.i.c ✓ 24
7.c even 3 1 5635.2.a.bc 12
7.d odd 6 1 5635.2.a.bd 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.i.c ✓ 24 1.a even 1 1 trivial
805.2.i.c ✓ 24 7.c even 3 1 inner
5635.2.a.bc 12 7.c even 3 1
5635.2.a.bd 12 7.d odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} - 7 T_{2}^{23} + 40 T_{2}^{22} - 137 T_{2}^{21} + 434 T_{2}^{20} - 1018 T_{2}^{19} + \cdots + 225 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display