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Properties

Label 805.2.u.c
Level $805$
Weight $2$
Character orbit 805.u
Analytic conductor $6.428$
Analytic rank $0$
Dimension $130$
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(36,805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(805, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("805.36");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.u (of order \(11\), degree \(10\), 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: \(130\)
Relative dimension: \(13\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 130 q - 2 q^{2} - 2 q^{3} - 16 q^{4} + 13 q^{5} + q^{6} + 13 q^{7} + 13 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 130 q - 2 q^{2} - 2 q^{3} - 16 q^{4} + 13 q^{5} + q^{6} + 13 q^{7} + 13 q^{8} - 3 q^{9} + 2 q^{10} - 2 q^{11} - 17 q^{12} - 17 q^{13} + 2 q^{14} + 2 q^{15} + 66 q^{16} + 37 q^{17} + 5 q^{18} - 5 q^{19} + 16 q^{20} + 2 q^{21} - 98 q^{22} + 6 q^{23} + 88 q^{24} - 13 q^{25} - 39 q^{26} - 2 q^{27} + 27 q^{28} - 21 q^{29} - q^{30} - 32 q^{31} - 30 q^{32} + 42 q^{33} - 3 q^{34} - 13 q^{35} - 139 q^{36} + 12 q^{37} - 4 q^{38} - 10 q^{39} - 35 q^{40} - 30 q^{41} - q^{42} - 6 q^{43} - 28 q^{44} - 162 q^{45} + 42 q^{46} + 54 q^{47} - 98 q^{48} - 13 q^{49} - 2 q^{50} - 30 q^{51} + 9 q^{52} + 2 q^{53} - 218 q^{54} - 9 q^{55} + 9 q^{56} - 45 q^{57} + 50 q^{58} - 82 q^{59} + 6 q^{60} + 56 q^{61} + 76 q^{62} + 25 q^{63} + 15 q^{64} + 6 q^{65} + 10 q^{66} - 34 q^{67} - 70 q^{68} + 40 q^{69} - 2 q^{70} - 16 q^{71} + 135 q^{72} - 80 q^{73} + 51 q^{74} - 2 q^{75} - 36 q^{76} - 9 q^{77} + 222 q^{78} + 62 q^{79} + 33 q^{80} + 15 q^{81} - 109 q^{82} - 41 q^{83} - 60 q^{84} + 7 q^{85} - 18 q^{86} - q^{87} + 24 q^{88} - 11 q^{89} + 94 q^{90} - 38 q^{91} + 76 q^{92} - 134 q^{93} + 37 q^{94} - 6 q^{95} - 95 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
36.1 −1.58087 − 1.82442i 0.749311 + 0.481553i −0.544736 + 3.78872i −0.415415 + 0.909632i −0.306008 − 2.12834i 0.959493 + 0.281733i 3.71172 − 2.38538i −0.916671 − 2.00723i 2.31627 − 0.680119i
36.2 −1.54061 − 1.77796i 2.19470 + 1.41045i −0.503033 + 3.49867i −0.415415 + 0.909632i −0.873460 − 6.07505i 0.959493 + 0.281733i 3.03726 − 1.95193i 1.58109 + 3.46211i 2.25729 − 0.662799i
36.3 −1.18643 − 1.36921i −2.80455 − 1.80237i −0.182497 + 1.26929i −0.415415 + 0.909632i 0.859564 + 5.97840i 0.959493 + 0.281733i −1.09379 + 0.702938i 3.37070 + 7.38080i 1.73834 − 0.510422i
36.4 −1.02402 − 1.18178i −0.00320548 − 0.00206004i −0.0633626 + 0.440696i −0.415415 + 0.909632i 0.000847963 0.00589771i 0.959493 + 0.281733i −2.04528 + 1.31442i −1.24624 − 2.72888i 1.50038 − 0.440552i
36.5 −0.760249 − 0.877375i −1.30759 − 0.840340i 0.0928227 − 0.645596i −0.415415 + 0.909632i 0.256805 + 1.78612i 0.959493 + 0.281733i −2.59028 + 1.66467i −0.242613 − 0.531248i 1.11391 − 0.327073i
36.6 −0.586494 − 0.676850i 2.32265 + 1.49268i 0.170479 − 1.18571i −0.415415 + 0.909632i −0.351902 − 2.44753i 0.959493 + 0.281733i −2.40938 + 1.54842i 1.92038 + 4.20504i 0.859323 − 0.252320i
36.7 −0.0503169 − 0.0580687i 0.515157 + 0.331071i 0.283789 − 1.97380i −0.415415 + 0.909632i −0.00669618 − 0.0465730i 0.959493 + 0.281733i −0.258172 + 0.165917i −1.09047 − 2.38779i 0.0737236 − 0.0216472i
36.8 0.0514308 + 0.0593543i −1.71683 − 1.10334i 0.283752 − 1.97354i −0.415415 + 0.909632i −0.0228100 − 0.158647i 0.959493 + 0.281733i 0.263870 − 0.169579i 0.483901 + 1.05959i −0.0753556 + 0.0221264i
36.9 0.768492 + 0.886888i 2.42979 + 1.56153i 0.0886408 − 0.616510i −0.415415 + 0.909632i 0.482372 + 3.35497i 0.959493 + 0.281733i 2.58935 − 1.66408i 2.21925 + 4.85947i −1.12598 + 0.330619i
36.10 0.811687 + 0.936737i 0.624828 + 0.401553i 0.0659896 − 0.458968i −0.415415 + 0.909632i 0.131016 + 0.911235i 0.959493 + 0.281733i 2.56893 − 1.65095i −1.01708 − 2.22709i −1.18927 + 0.349202i
36.11 0.882640 + 1.01862i −2.20607 − 1.41775i 0.0260948 − 0.181494i −0.415415 + 0.909632i −0.503009 − 3.49851i 0.959493 + 0.281733i 2.47564 − 1.59099i 1.61046 + 3.52641i −1.29323 + 0.379727i
36.12 1.45194 + 1.67562i −0.943609 − 0.606421i −0.414966 + 2.88615i −0.415415 + 0.909632i −0.353927 − 2.46162i 0.959493 + 0.281733i −1.70821 + 1.09780i −0.723593 − 1.58445i −2.12736 + 0.624648i
36.13 1.66100 + 1.91690i 1.82793 + 1.17474i −0.630941 + 4.38829i −0.415415 + 0.909632i 0.784338 + 5.45519i 0.959493 + 0.281733i −5.19236 + 3.33693i 0.715068 + 1.56578i −2.43368 + 0.714592i
71.1 −2.11276 − 1.35779i −0.465247 − 3.23586i 1.78933 + 3.91809i 0.959493 + 0.281733i −3.41066 + 7.46830i 0.654861 − 0.755750i 0.824679 − 5.73577i −7.37586 + 2.16575i −1.64464 − 1.89802i
71.2 −2.00693 − 1.28977i 0.446718 + 3.10699i 1.53341 + 3.35771i 0.959493 + 0.281733i 3.11079 − 6.81167i 0.654861 − 0.755750i 0.574211 − 3.99373i −6.57535 + 1.93070i −1.56226 − 1.80295i
71.3 −1.70284 − 1.09435i 0.222561 + 1.54795i 0.871226 + 1.90772i 0.959493 + 0.281733i 1.31501 − 2.87946i 0.654861 − 0.755750i 0.0280127 − 0.194832i 0.531866 − 0.156170i −1.32555 − 1.52976i
71.4 −1.35479 − 0.870669i −0.199294 − 1.38612i 0.246555 + 0.539881i 0.959493 + 0.281733i −0.936851 + 2.05142i 0.654861 − 0.755750i −0.322351 + 2.24200i 0.996869 − 0.292707i −1.05461 − 1.21709i
71.5 −0.927276 − 0.595924i 0.0324735 + 0.225858i −0.326115 − 0.714092i 0.959493 + 0.281733i 0.104482 − 0.228785i 0.654861 − 0.755750i −0.436881 + 3.03857i 2.82852 − 0.830529i −0.721824 − 0.833029i
71.6 −0.174827 − 0.112355i −0.188009 − 1.30763i −0.812889 − 1.77998i 0.959493 + 0.281733i −0.114049 + 0.249733i 0.654861 − 0.755750i −0.117025 + 0.813926i 1.20393 − 0.353506i −0.136092 − 0.157058i
71.7 −0.0543920 − 0.0349556i 0.310763 + 2.16141i −0.829093 − 1.81546i 0.959493 + 0.281733i 0.0586503 − 0.128426i 0.654861 − 0.755750i −0.0367675 + 0.255724i −1.69663 + 0.498175i −0.0423406 − 0.0488637i
See next 80 embeddings (of 130 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 36.13
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 805.2.u.c ✓ 130
23.c even 11 1 inner 805.2.u.c ✓ 130
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
805.2.u.c ✓ 130 1.a even 1 1 trivial
805.2.u.c ✓ 130 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{130} + 2 T_{2}^{129} + 23 T_{2}^{128} + 27 T_{2}^{127} + 231 T_{2}^{126} + 123 T_{2}^{125} + \cdots + 529 \) acting on \(S_{2}^{\mathrm{new}}(805, [\chi])\). Copy content Toggle raw display