Properties

Label 6023.2.a.a
Level $6023$
Weight $2$
Character orbit 6023.a
Self dual yes
Analytic conductor $48.094$
Analytic rank $1$
Dimension $98$
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: \(1\)
Dimension: \(98\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.78159 0.980083 5.73723 −2.26646 −2.72619 0.130985 −10.3954 −2.03944 6.30436
1.2 −2.72324 −3.03839 5.41603 −0.824121 8.27426 −3.50609 −9.30267 6.23182 2.24428
1.3 −2.72317 −0.516928 5.41568 3.12322 1.40769 −3.06631 −9.30149 −2.73279 −8.50508
1.4 −2.63244 −2.81028 4.92974 1.41252 7.39789 3.18061 −7.71236 4.89767 −3.71838
1.5 −2.52650 1.56416 4.38319 1.08994 −3.95184 4.94624 −6.02111 −0.553409 −2.75372
1.6 −2.52400 −0.270526 4.37060 −2.19505 0.682808 −4.06184 −5.98340 −2.92682 5.54031
1.7 −2.51733 −2.83375 4.33693 3.33686 7.13347 2.06105 −5.88281 5.03014 −8.39997
1.8 −2.51387 −0.144321 4.31953 2.01567 0.362803 1.13174 −5.83100 −2.97917 −5.06713
1.9 −2.51046 3.07291 4.30243 0.528149 −7.71443 −0.975247 −5.78017 6.44278 −1.32590
1.10 −2.36387 −1.85446 3.58790 −2.76467 4.38371 3.05083 −3.75360 0.439017 6.53534
1.11 −2.30301 −0.172789 3.30385 −0.809544 0.397934 0.778568 −3.00278 −2.97014 1.86439
1.12 −2.23585 2.07159 2.99900 2.91944 −4.63176 −1.89696 −2.23362 1.29150 −6.52741
1.13 −2.22980 2.83472 2.97200 −0.749386 −6.32084 0.730492 −2.16735 5.03561 1.67098
1.14 −2.16233 −1.79610 2.67567 −1.92302 3.88377 3.63289 −1.46101 0.225992 4.15820
1.15 −2.15437 −1.80294 2.64131 1.24504 3.88420 −4.16426 −1.38162 0.250590 −2.68227
1.16 −2.11992 0.896090 2.49404 2.73729 −1.89963 −3.12431 −1.04733 −2.19702 −5.80282
1.17 −2.03453 −2.81750 2.13929 −2.44691 5.73228 −2.76718 −0.283395 4.93833 4.97829
1.18 −2.01585 1.02156 2.06364 0.907276 −2.05931 1.44669 −0.128285 −1.95642 −1.82893
1.19 −1.95295 2.01904 1.81400 −3.44278 −3.94307 −1.14802 0.363246 1.07651 6.72357
1.20 −1.88657 −2.34604 1.55916 1.12157 4.42598 2.57604 0.831673 2.50392 −2.11593
See all 98 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.98
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.a 98
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6023.2.a.a 98 1.a even 1 1 trivial