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Properties

Label 2023.4.a.u
Level $2023$
Weight $4$
Character orbit 2023.a
Self dual yes
Analytic conductor $119.361$
Analytic rank $1$
Dimension $56$
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: \(1\)
Dimension: \(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56 q + 8 q^{2} - 24 q^{3} + 240 q^{4} - 80 q^{5} - 68 q^{6} - 392 q^{7} + 96 q^{8} + 576 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 56 q + 8 q^{2} - 24 q^{3} + 240 q^{4} - 80 q^{5} - 68 q^{6} - 392 q^{7} + 96 q^{8} + 576 q^{9} - 80 q^{10} - 176 q^{11} - 288 q^{12} - 96 q^{13} - 56 q^{14} + 192 q^{15} + 1088 q^{16} + 216 q^{18} + 48 q^{19} - 1660 q^{20} + 168 q^{21} - 352 q^{22} - 608 q^{23} - 736 q^{24} + 1792 q^{25} - 864 q^{27} - 1680 q^{28} - 928 q^{29} - 100 q^{30} - 496 q^{31} + 436 q^{32} + 384 q^{33} + 560 q^{35} + 2804 q^{36} - 1392 q^{37} - 624 q^{39} + 1020 q^{40} - 2088 q^{41} + 476 q^{42} + 1312 q^{43} - 2112 q^{44} - 4840 q^{45} - 736 q^{46} - 5228 q^{48} + 2744 q^{49} + 2020 q^{50} - 1536 q^{52} + 1272 q^{53} - 2268 q^{54} - 336 q^{55} - 672 q^{56} - 2448 q^{57} - 1376 q^{58} + 2372 q^{60} - 976 q^{61} - 3776 q^{62} - 4032 q^{63} + 5376 q^{64} - 6080 q^{65} + 976 q^{67} + 1248 q^{69} + 560 q^{70} - 3216 q^{71} + 4532 q^{72} - 4088 q^{73} + 2456 q^{74} + 760 q^{75} - 2640 q^{76} + 1232 q^{77} - 3744 q^{78} - 1792 q^{79} - 13920 q^{80} + 4184 q^{81} - 8204 q^{82} - 2832 q^{83} + 2016 q^{84} + 4908 q^{86} + 832 q^{87} - 2424 q^{88} - 2768 q^{89} - 8660 q^{90} + 672 q^{91} - 6784 q^{92} + 784 q^{93} - 928 q^{94} - 4560 q^{95} - 6656 q^{96} - 9464 q^{97} + 392 q^{98} - 6576 q^{99}+O(q^{100}) \) 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 −5.44250 3.50764 21.6208 −17.6325 −19.0903 −7.00000 −74.1312 −14.6965 95.9646
1.2 −5.37158 −8.74313 20.8539 −18.6028 46.9644 −7.00000 −69.0459 49.4422 99.9265
1.3 −5.34059 −1.34087 20.5219 −12.2041 7.16104 −7.00000 −66.8743 −25.2021 65.1771
1.4 −5.09246 −3.97226 17.9331 −1.01975 20.2285 −7.00000 −50.5840 −11.2212 5.19304
1.5 −4.88913 5.33007 15.9036 4.56956 −26.0594 −7.00000 −38.6415 1.40966 −22.3412
1.6 −4.80359 −3.56192 15.0745 13.7155 17.1100 −7.00000 −33.9829 −14.3127 −65.8837
1.7 −4.58987 8.72454 13.0669 9.48008 −40.0445 −7.00000 −23.2564 49.1175 −43.5123
1.8 −4.18078 9.88314 9.47894 −15.9203 −41.3193 −7.00000 −6.18312 70.6765 66.5594
1.9 −4.15313 −6.23473 9.24849 −6.11880 25.8936 −7.00000 −5.18513 11.8718 25.4122
1.10 −4.02697 −5.00456 8.21652 11.3608 20.1532 −7.00000 −0.871912 −1.95434 −45.7495
1.11 −3.70056 0.163285 5.69418 −1.64582 −0.604248 −7.00000 8.53285 −26.9733 6.09048
1.12 −3.64206 6.07912 5.26462 0.735620 −22.1405 −7.00000 9.96243 9.95570 −2.67917
1.13 −3.45966 −9.80544 3.96924 −8.21567 33.9235 −7.00000 13.9451 69.1466 28.4234
1.14 −2.84143 4.61772 0.0737140 −1.51243 −13.1209 −7.00000 22.5220 −5.67667 4.29745
1.15 −2.82994 6.04539 0.00856474 19.0541 −17.1081 −7.00000 22.6153 9.54677 −53.9220
1.16 −2.59498 8.23188 −1.26609 −17.1201 −21.3616 −7.00000 24.0453 40.7639 44.4262
1.17 −2.54086 −6.70229 −1.54403 −12.1786 17.0296 −7.00000 24.2500 17.9207 30.9441
1.18 −2.52696 −2.34010 −1.61447 −8.71902 5.91333 −7.00000 24.2954 −21.5240 22.0326
1.19 −2.10637 −2.26967 −3.56319 20.8742 4.78078 −7.00000 24.3564 −21.8486 −43.9688
1.20 −1.91072 3.61256 −4.34916 15.8569 −6.90258 −7.00000 23.5957 −13.9494 −30.2981
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.56
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.u 56
17.b even 2 1 2023.4.a.v 56
17.e odd 16 2 119.4.k.a ✓ 112
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
119.4.k.a ✓ 112 17.e odd 16 2
2023.4.a.u 56 1.a even 1 1 trivial
2023.4.a.v 56 17.b even 2 1

Hecke kernels

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

\( T_{2}^{56} - 8 T_{2}^{55} - 312 T_{2}^{54} + 2592 T_{2}^{53} + 45424 T_{2}^{52} - 394148 T_{2}^{51} + \cdots - 18\!\cdots\!48 \) Copy content Toggle raw display
\( T_{3}^{56} + 24 T_{3}^{55} - 756 T_{3}^{54} - 22032 T_{3}^{53} + 242278 T_{3}^{52} + \cdots - 34\!\cdots\!88 \) Copy content Toggle raw display