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Properties

Label 2023.4.a.t
Level $2023$
Weight $4$
Character orbit 2023.a
Self dual yes
Analytic conductor $119.361$
Analytic rank $0$
Dimension $39$
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] = [2023,4,Mod(1,2023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2023, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2023.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2023.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: \(119.360863942\)
Analytic rank: \(0\)
Dimension: \(39\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 39 q + 12 q^{2} + 168 q^{4} + 60 q^{6} - 273 q^{7} + 159 q^{8} + 459 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 39 q + 12 q^{2} + 168 q^{4} + 60 q^{6} - 273 q^{7} + 159 q^{8} + 459 q^{9} - 249 q^{11} + 228 q^{13} - 84 q^{14} + 552 q^{15} + 768 q^{16} - 33 q^{18} + 78 q^{19} + 876 q^{20} - 456 q^{22} - 444 q^{23} + 1041 q^{24} + 1065 q^{25} + 60 q^{26} - 444 q^{27} - 1176 q^{28} - 930 q^{29} + 1611 q^{30} + 54 q^{31} + 2064 q^{32} + 594 q^{33} + 3306 q^{36} - 66 q^{37} + 1761 q^{38} - 1392 q^{39} - 1485 q^{40} + 150 q^{41} - 420 q^{42} + 774 q^{43} - 3144 q^{44} + 2148 q^{45} - 1335 q^{46} + 2382 q^{47} + 1905 q^{48} + 1911 q^{49} + 627 q^{50} + 1335 q^{52} + 2238 q^{53} + 1620 q^{54} + 984 q^{55} - 1113 q^{56} - 1584 q^{57} + 2367 q^{58} + 2526 q^{59} + 4719 q^{60} - 1896 q^{61} - 321 q^{62} - 3213 q^{63} + 6849 q^{64} - 3204 q^{65} - 348 q^{66} + 2943 q^{67} - 300 q^{69} - 2946 q^{71} + 252 q^{72} - 1530 q^{73} - 24 q^{74} + 2430 q^{75} - 4176 q^{76} + 1743 q^{77} + 1788 q^{78} + 780 q^{79} + 8283 q^{80} + 8727 q^{81} + 9099 q^{82} + 3486 q^{83} + 3273 q^{86} + 852 q^{87} - 3030 q^{88} + 4518 q^{89} + 7323 q^{90} - 1596 q^{91} + 4392 q^{92} + 3036 q^{93} + 2040 q^{94} - 2874 q^{95} + 17592 q^{96} + 6780 q^{97} + 588 q^{98} - 3153 q^{99}+O(q^{100}) \) 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 −5.31325 2.71999 20.2306 17.7320 −14.4520 −7.00000 −64.9842 −19.6017 −94.2143
1.2 −5.24716 −9.81353 19.5326 6.47604 51.4931 −7.00000 −60.5136 69.3054 −33.9808
1.3 −4.93527 −0.435230 16.3569 −4.99873 2.14798 −7.00000 −41.2436 −26.8106 24.6701
1.4 −4.67254 −8.54284 13.8326 0.412709 39.9168 −7.00000 −27.2533 45.9801 −1.92840
1.5 −4.38659 10.0770 11.2422 13.3482 −44.2037 −7.00000 −14.2220 74.5462 −58.5528
1.6 −4.00433 6.70674 8.03466 −13.9164 −26.8560 −7.00000 −0.138805 17.9803 55.7257
1.7 −3.44509 −7.21270 3.86864 13.0773 24.8484 −7.00000 14.2329 25.0231 −45.0525
1.8 −3.40099 1.52322 3.56675 7.49481 −5.18046 −7.00000 15.0775 −24.6798 −25.4898
1.9 −3.35305 −3.55945 3.24293 8.23286 11.9350 −7.00000 15.9507 −14.3303 −27.6052
1.10 −3.04820 0.283925 1.29150 −14.1692 −0.865460 −7.00000 20.4488 −26.9194 43.1906
1.11 −2.91293 6.77923 0.485184 −0.721673 −19.7475 −7.00000 21.8902 18.9580 2.10219
1.12 −2.73740 −8.19137 −0.506648 −19.8266 22.4231 −7.00000 23.2861 40.0986 54.2732
1.13 −2.59502 6.97596 −1.26587 −11.8702 −18.1028 −7.00000 24.0451 21.6641 30.8035
1.14 −1.26953 −3.73786 −6.38830 −19.4703 4.74531 −7.00000 18.2663 −13.0284 24.7180
1.15 −0.950553 −1.82005 −7.09645 8.63683 1.73005 −7.00000 14.3500 −23.6874 −8.20977
1.16 −0.895868 −5.59937 −7.19742 6.01681 5.01629 −7.00000 13.6149 4.35290 −5.39027
1.17 −0.469895 4.61024 −7.77920 16.5057 −2.16633 −7.00000 7.41457 −5.74571 −7.75596
1.18 −0.364785 −9.16874 −7.86693 −18.8389 3.34461 −7.00000 5.78801 57.0657 6.87214
1.19 −0.270765 4.12008 −7.92669 1.98119 −1.11557 −7.00000 4.31239 −10.0250 −0.536438
1.20 −0.0442302 6.66763 −7.99804 −20.1798 −0.294911 −7.00000 0.707597 17.4573 0.892557
See all 39 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.39
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(17\) \(1\)

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 2023.4.a.t yes 39
17.b even 2 1 2023.4.a.s ✓ 39
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2023.4.a.s ✓ 39 17.b even 2 1
2023.4.a.t yes 39 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\):

\( T_{2}^{39} - 12 T_{2}^{38} - 168 T_{2}^{37} + 2475 T_{2}^{36} + 11340 T_{2}^{35} + \cdots - 142689053454336 \) Copy content Toggle raw display
\( T_{3}^{39} - 756 T_{3}^{37} + 148 T_{3}^{36} + 260076 T_{3}^{35} - 107730 T_{3}^{34} + \cdots + 16\!\cdots\!08 \) Copy content Toggle raw display