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Properties

Label 2023.4.a.p
Level $2023$
Weight $4$
Character orbit 2023.a
Self dual yes
Analytic conductor $119.361$
Analytic rank $0$
Dimension $26$
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: \(26\)
Twist minimal: no (minimal twist has level 119)
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.

\(\operatorname{Tr}(f)(q) = \) \( 26 q - 8 q^{2} + 12 q^{3} + 96 q^{4} + 40 q^{5} + 14 q^{6} - 182 q^{7} - 96 q^{8} + 230 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 26 q - 8 q^{2} + 12 q^{3} + 96 q^{4} + 40 q^{5} + 14 q^{6} - 182 q^{7} - 96 q^{8} + 230 q^{9} + 40 q^{10} + 88 q^{11} + 4 q^{12} - 32 q^{13} + 56 q^{14} - 144 q^{15} + 56 q^{16} - 288 q^{18} + 204 q^{19} - 30 q^{20} - 84 q^{21} + 176 q^{22} + 752 q^{23} + 208 q^{24} + 718 q^{25} + 432 q^{27} - 672 q^{28} + 288 q^{29} - 530 q^{30} + 176 q^{31} - 1126 q^{32} - 612 q^{33} - 280 q^{35} + 834 q^{36} + 488 q^{37} - 164 q^{38} + 1480 q^{39} + 2298 q^{40} + 1252 q^{41} - 98 q^{42} - 32 q^{43} + 1056 q^{44} + 260 q^{45} - 2128 q^{46} + 760 q^{47} - 1046 q^{48} + 1274 q^{49} - 862 q^{50} - 512 q^{52} - 636 q^{53} + 594 q^{54} - 168 q^{55} + 672 q^{56} + 2520 q^{57} + 1168 q^{58} - 440 q^{59} + 2806 q^{60} + 488 q^{61} + 4252 q^{62} - 1610 q^{63} - 24 q^{64} + 976 q^{65} - 424 q^{66} - 560 q^{67} + 848 q^{69} - 280 q^{70} + 1800 q^{71} - 42 q^{72} + 3916 q^{73} + 2628 q^{74} + 7628 q^{75} + 1272 q^{76} - 616 q^{77} + 1872 q^{78} + 1904 q^{79} - 4300 q^{80} - 1354 q^{81} - 3638 q^{82} + 536 q^{83} - 28 q^{84} - 186 q^{86} + 2632 q^{87} + 3012 q^{88} - 336 q^{89} + 326 q^{90} + 224 q^{91} + 10560 q^{92} - 1704 q^{93} + 1408 q^{94} + 4264 q^{95} + 7104 q^{96} + 812 q^{97} - 392 q^{98} - 5352 q^{99}+O(q^{100}) \) 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 −5.54560 −3.83184 22.7537 −1.51739 21.2498 −7.00000 −81.8179 −12.3170 8.41486
1.2 −5.13049 −5.92819 18.3219 −15.1032 30.4145 −7.00000 −52.9565 8.14343 77.4870
1.3 −4.85775 8.06106 15.5978 −14.5084 −39.1587 −7.00000 −36.9080 37.9807 70.4783
1.4 −4.35588 4.10426 10.9737 −6.71238 −17.8777 −7.00000 −12.9532 −10.1550 29.2384
1.5 −4.27038 8.00973 10.2362 21.4822 −34.2046 −7.00000 −9.54927 37.1559 −91.7372
1.6 −4.01439 −4.10038 8.11536 10.7461 16.4605 −7.00000 −0.463085 −10.1869 −43.1392
1.7 −3.46502 −9.62151 4.00634 7.83007 33.3387 −7.00000 13.8381 65.5735 −27.1313
1.8 −3.12639 0.659242 1.77429 20.8519 −2.06104 −7.00000 19.4640 −26.5654 −65.1910
1.9 −2.56998 8.63556 −1.39520 9.68821 −22.1932 −7.00000 24.1455 47.5729 −24.8985
1.10 −1.78790 1.05883 −4.80342 −13.6640 −1.89309 −7.00000 22.8912 −25.8789 24.4298
1.11 −1.77604 −7.68104 −4.84567 −0.0449169 13.6419 −7.00000 22.8145 31.9984 0.0797743
1.12 −1.61350 5.03254 −5.39661 −11.1388 −8.12002 −7.00000 21.6155 −1.67351 17.9725
1.13 −0.986805 4.93329 −7.02622 8.38060 −4.86820 −7.00000 14.8279 −2.66264 −8.27002
1.14 −0.543251 −7.07568 −7.70488 −4.14039 3.84387 −7.00000 8.53169 23.0653 2.24927
1.15 0.751064 −3.95050 −7.43590 20.7136 −2.96708 −7.00000 −11.5933 −11.3935 15.5573
1.16 0.997246 0.896049 −7.00550 7.48135 0.893581 −7.00000 −14.9642 −26.1971 7.46074
1.17 1.50705 7.95342 −5.72879 −5.46957 11.9862 −7.00000 −20.6900 36.2569 −8.24294
1.18 2.23074 9.35531 −3.02379 −20.3178 20.8693 −7.00000 −24.5912 60.5219 −45.3238
1.19 2.38962 −4.73294 −2.28972 6.08975 −11.3099 −7.00000 −24.5885 −4.59930 14.5522
1.20 2.69417 1.13871 −0.741449 4.85132 3.06788 −7.00000 −23.5509 −25.7033 13.0703
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
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.p 26
17.b even 2 1 2023.4.a.o 26
17.d even 8 2 119.4.g.a ✓ 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.4.g.a ✓ 52 17.d even 8 2
2023.4.a.o 26 17.b even 2 1
2023.4.a.p 26 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\):

\( T_{2}^{26} + 8 T_{2}^{25} - 120 T_{2}^{24} - 1056 T_{2}^{23} + 6034 T_{2}^{22} + 60734 T_{2}^{21} + \cdots + 71967262976 \) Copy content Toggle raw display
\( T_{3}^{26} - 12 T_{3}^{25} - 394 T_{3}^{24} + 4944 T_{3}^{23} + 66414 T_{3}^{22} - 877864 T_{3}^{21} + \cdots - 21\!\cdots\!96 \) Copy content Toggle raw display