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Properties

Label 6023.2.a.d
Level $6023$
Weight $2$
Character orbit 6023.a
Self dual yes
Analytic conductor $48.094$
Analytic rank $0$
Dimension $140$
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] = [6023,2,Mod(1,6023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6023, 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("6023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6023 = 19 \cdot 317 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6023.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: \(48.0938971374\)
Analytic rank: \(0\)
Dimension: \(140\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 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 −2.81146 3.38830 5.90432 1.31579 −9.52607 1.88433 −10.9768 8.48057 −3.69930
1.2 −2.77997 −2.09006 5.72822 0.541434 5.81030 4.43063 −10.3643 1.36835 −1.50517
1.3 −2.76348 −3.02907 5.63680 4.42510 8.37075 −1.32943 −10.0502 6.17524 −12.2287
1.4 −2.74325 1.84551 5.52540 −2.64274 −5.06270 −2.21393 −9.67106 0.405925 7.24969
1.5 −2.71272 −1.70174 5.35887 −3.51340 4.61635 3.49913 −9.11167 −0.104083 9.53088
1.6 −2.67904 −0.649743 5.17727 −3.70919 1.74069 −4.64503 −8.51205 −2.57783 9.93707
1.7 −2.62272 0.254820 4.87868 4.28261 −0.668323 3.95531 −7.54997 −2.93507 −11.2321
1.8 −2.59629 2.14678 4.74071 −3.36546 −5.57365 2.25359 −7.11569 1.60865 8.73769
1.9 −2.57318 −1.88947 4.62125 −0.577572 4.86195 −3.88708 −6.74496 0.570108 1.48620
1.10 −2.56765 0.729440 4.59285 −3.21691 −1.87295 3.04493 −6.65754 −2.46792 8.25992
1.11 −2.54565 1.89511 4.48036 0.316502 −4.82430 4.66425 −6.31414 0.591450 −0.805706
1.12 −2.51714 −1.59250 4.33600 3.04640 4.00854 0.234755 −5.88004 −0.463957 −7.66821
1.13 −2.50460 −0.513198 4.27304 1.36674 1.28536 −1.89861 −5.69306 −2.73663 −3.42314
1.14 −2.48608 −2.16516 4.18058 −0.720530 5.38275 −0.0570474 −5.42110 1.68791 1.79129
1.15 −2.46064 3.05601 4.05473 4.13558 −7.51973 −4.22732 −5.05594 6.33922 −10.1762
1.16 −2.37815 0.382823 3.65560 3.62895 −0.910412 −2.15818 −3.93728 −2.85345 −8.63020
1.17 −2.34544 0.814980 3.50107 0.397454 −1.91148 −3.87514 −3.52066 −2.33581 −0.932204
1.18 −2.24180 −2.80359 3.02567 1.63656 6.28509 0.514582 −2.29934 4.86012 −3.66885
1.19 −2.20474 −3.27519 2.86088 −2.46837 7.22094 4.00346 −1.89803 7.72686 5.44211
1.20 −2.12238 2.91250 2.50448 1.81666 −6.18142 0.226771 −1.07071 5.48264 −3.85564
See next 80 embeddings (of 140 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.140
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(19\) \(1\)
\(317\) \(-1\)

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 6023.2.a.d ✓ 140
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6023.2.a.d ✓ 140 1.a even 1 1 trivial