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Properties

Label 2669.2.a.c
Level $2669$
Weight $2$
Character orbit 2669.a
Self dual yes
Analytic conductor $21.312$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2669,2,Mod(1,2669)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2669, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2669.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2669 = 17 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2669.a (trivial)

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: yes
Analytic conductor: \(21.3120722995\)
Analytic rank: \(0\)
Dimension: \(60\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q + q^{2} + 24 q^{3} + 75 q^{4} + 12 q^{5} + 2 q^{6} + 12 q^{7} - 6 q^{8} + 74 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 60 q + q^{2} + 24 q^{3} + 75 q^{4} + 12 q^{5} + 2 q^{6} + 12 q^{7} - 6 q^{8} + 74 q^{9} + 21 q^{10} + 34 q^{11} + 45 q^{12} + 20 q^{13} + 25 q^{14} + 6 q^{15} + 101 q^{16} + 60 q^{17} - 12 q^{18} + 68 q^{19} + 16 q^{20} + 10 q^{21} + 13 q^{22} + 26 q^{23} - 11 q^{24} + 76 q^{25} - 16 q^{26} + 81 q^{27} + 15 q^{28} + 17 q^{29} - 27 q^{30} + 71 q^{31} - 21 q^{32} + 4 q^{33} + q^{34} + 8 q^{35} + 97 q^{36} + 20 q^{37} - 18 q^{38} + 15 q^{39} + 58 q^{40} + 29 q^{41} - 9 q^{42} + 29 q^{43} + 31 q^{44} + 9 q^{45} + 46 q^{46} + 19 q^{47} + 62 q^{48} + 94 q^{49} - 37 q^{50} + 24 q^{51} + 27 q^{52} - 7 q^{53} + 2 q^{54} + 37 q^{55} + 34 q^{56} + 31 q^{57} + 32 q^{58} + 59 q^{59} - 67 q^{60} + 46 q^{61} + 2 q^{62} + 40 q^{63} + 154 q^{64} + 17 q^{65} + 113 q^{66} + 64 q^{67} + 75 q^{68} + 21 q^{69} - 22 q^{70} + 38 q^{71} - 24 q^{72} + 24 q^{73} + 59 q^{74} + 143 q^{75} + 169 q^{76} - 60 q^{77} - 15 q^{78} + 53 q^{79} + 79 q^{80} + 108 q^{81} + 12 q^{82} - 2 q^{83} - 50 q^{84} + 12 q^{85} - 30 q^{86} - 19 q^{87} + 3 q^{88} - 19 q^{89} - 57 q^{90} + 189 q^{91} + 96 q^{92} + 16 q^{93} - 8 q^{94} + 9 q^{95} - 23 q^{96} + 24 q^{97} - 12 q^{98} + 87 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.80018 −0.133707 5.84103 −2.99515 0.374404 −0.480124 −10.7556 −2.98212 8.38697
1.2 −2.77308 −2.55165 5.69000 1.20632 7.07595 −2.74802 −10.2327 3.51093 −3.34523
1.3 −2.72972 −0.508727 5.45136 −0.705507 1.38868 4.05786 −9.42125 −2.74120 1.92584
1.4 −2.68946 2.61669 5.23321 −3.62493 −7.03750 2.33999 −8.69560 3.84708 9.74912
1.5 −2.65915 3.40285 5.07109 3.47983 −9.04871 −0.870840 −8.16650 8.57941 −9.25339
1.6 −2.50461 1.33846 4.27305 4.07552 −3.35232 −4.70558 −5.69310 −1.20852 −10.2076
1.7 −2.42553 3.32245 3.88318 −3.13293 −8.05869 −4.52328 −4.56770 8.03868 7.59901
1.8 −2.31316 1.54271 3.35071 0.160514 −3.56853 3.95767 −3.12441 −0.620058 −0.371295
1.9 −2.17078 −1.31695 2.71227 −3.10959 2.85881 0.947293 −1.54618 −1.26564 6.75022
1.10 −2.11571 −0.986449 2.47622 2.56516 2.08704 3.50157 −1.00753 −2.02692 −5.42713
1.11 −2.07858 −0.428702 2.32052 0.205414 0.891094 −3.64053 −0.666218 −2.81621 −0.426971
1.12 −2.07826 −2.85099 2.31917 2.30338 5.92510 0.674312 −0.663323 5.12814 −4.78702
1.13 −2.03667 1.62313 2.14804 4.03443 −3.30579 3.18743 −0.301504 −0.365444 −8.21682
1.14 −1.77407 2.44733 1.14732 1.81512 −4.34174 −1.07975 1.51271 2.98943 −3.22014
1.15 −1.74259 0.913636 1.03661 −3.06996 −1.59209 −2.65224 1.67880 −2.16527 5.34967
1.16 −1.62752 −2.41860 0.648809 −3.30279 3.93631 −2.85756 2.19909 2.84963 5.37534
1.17 −1.51462 −0.584534 0.294065 0.309597 0.885345 −2.29590 2.58384 −2.65832 −0.468921
1.18 −1.36297 −2.84741 −0.142302 −2.57628 3.88094 1.70499 2.91990 5.10773 3.51140
1.19 −1.34018 1.68664 −0.203928 −2.74895 −2.26040 3.42892 2.95365 −0.155235 3.68408
1.20 −1.26033 3.30411 −0.411578 −1.62739 −4.16426 −0.732760 3.03937 7.91716 2.05104
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.60
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(17\) \(-1\)
\(157\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2669.2.a.c ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2669.2.a.c ✓ 60 1.a even 1 1 trivial