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Properties

Label 2023.4.a.r
Level $2023$
Weight $4$
Character orbit 2023.a
Self dual yes
Analytic conductor $119.361$
Analytic rank $1$
Dimension $33$
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: \(33\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 33 q - 12 q^{2} + 120 q^{4} + 30 q^{6} + 231 q^{7} - 108 q^{8} + 189 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 33 q - 12 q^{2} + 120 q^{4} + 30 q^{6} + 231 q^{7} - 108 q^{8} + 189 q^{9} - 45 q^{11} - 84 q^{13} - 84 q^{14} - 276 q^{15} + 384 q^{16} - 681 q^{18} - 150 q^{19} - 414 q^{20} - 456 q^{22} - 252 q^{23} - 321 q^{24} + 447 q^{25} - 876 q^{26} - 444 q^{27} + 840 q^{28} - 114 q^{29} + 891 q^{30} + 54 q^{31} - 456 q^{32} - 1782 q^{33} + 1146 q^{36} - 378 q^{37} - 2169 q^{38} - 1392 q^{39} + 1485 q^{40} - 150 q^{41} + 210 q^{42} - 1914 q^{43} - 1512 q^{44} - 2892 q^{45} - 774 q^{46} - 1770 q^{47} - 1905 q^{48} + 1617 q^{49} - 2373 q^{50} - 1785 q^{52} - 2850 q^{53} + 810 q^{54} - 480 q^{55} - 756 q^{56} + 216 q^{57} - 2268 q^{58} - 78 q^{59} - 3969 q^{60} + 1776 q^{61} - 2337 q^{62} + 1323 q^{63} - 1884 q^{64} - 2280 q^{65} + 348 q^{66} - 2493 q^{67} - 3612 q^{69} - 2658 q^{71} - 6579 q^{72} + 1530 q^{73} + 378 q^{74} + 4398 q^{75} + 3024 q^{76} - 315 q^{77} + 3828 q^{78} - 5520 q^{79} - 4587 q^{80} - 1791 q^{81} + 2769 q^{82} - 1506 q^{83} - 3690 q^{86} - 3324 q^{87} + 945 q^{88} - 5826 q^{89} + 8913 q^{90} - 588 q^{91} + 2109 q^{92} - 2796 q^{93} - 648 q^{94} - 2058 q^{95} + 6696 q^{96} + 2040 q^{97} - 588 q^{98} + 3291 q^{99}+O(q^{100}) \) 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 −5.52078 −9.38929 22.4790 −5.77676 51.8362 7.00000 −79.9352 61.1588 31.8922
1.2 −5.07941 −2.55228 17.8004 −3.71117 12.9641 7.00000 −49.7801 −20.4859 18.8506
1.3 −4.93834 8.94979 16.3872 −21.3321 −44.1971 7.00000 −41.4188 53.0987 105.345
1.4 −4.86513 7.74438 15.6695 −1.57923 −37.6775 7.00000 −37.3133 32.9755 7.68317
1.5 −4.53865 6.38567 12.5994 −3.92931 −28.9823 7.00000 −20.8750 13.7767 17.8338
1.6 −4.52262 −0.779905 12.4541 20.5366 3.52721 7.00000 −20.1440 −26.3917 −92.8792
1.7 −4.24717 −3.35597 10.0385 14.1927 14.2534 7.00000 −8.65770 −15.7374 −60.2787
1.8 −4.01913 −6.12390 8.15337 −12.2431 24.6127 7.00000 −0.616423 10.5021 49.2066
1.9 −3.32066 −1.47316 3.02677 −11.8964 4.89186 7.00000 16.5144 −24.8298 39.5039
1.10 −3.16835 −4.93332 2.03846 20.3351 15.6305 7.00000 18.8883 −2.66232 −64.4287
1.11 −2.63791 6.08905 −1.04141 6.01869 −16.0624 7.00000 23.8505 10.0765 −15.8768
1.12 −2.19156 2.06612 −3.19707 −3.10156 −4.52802 7.00000 24.5390 −22.7312 6.79725
1.13 −2.16203 4.73190 −3.32562 4.60805 −10.2305 7.00000 24.4863 −4.60912 −9.96276
1.14 −1.53862 −9.94675 −5.63264 −4.25563 15.3043 7.00000 20.9755 71.9377 6.54781
1.15 −1.31310 −8.52714 −6.27576 12.5675 11.1970 7.00000 18.7455 45.7121 −16.5024
1.16 −0.629496 −8.05991 −7.60374 2.93192 5.07368 7.00000 9.82248 37.9621 −1.84563
1.17 −0.274724 1.62606 −7.92453 20.2734 −0.446717 7.00000 4.37485 −24.3559 −5.56958
1.18 −0.270372 7.90101 −7.92690 −18.4164 −2.13622 7.00000 4.30619 35.4260 4.97929
1.19 0.00411295 0.527947 −7.99998 −15.2478 0.00217142 7.00000 −0.0658072 −26.7213 −0.0627133
1.20 0.629445 1.27281 −7.60380 8.75892 0.801167 7.00000 −9.82174 −25.3799 5.51326
See all 33 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.33
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.r yes 33
17.b even 2 1 2023.4.a.q ✓ 33
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2023.4.a.q ✓ 33 17.b even 2 1
2023.4.a.r yes 33 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2023))\):

\( T_{2}^{33} + 12 T_{2}^{32} - 120 T_{2}^{31} - 1916 T_{2}^{30} + 4800 T_{2}^{29} + 135048 T_{2}^{28} + \cdots - 11194773504 \) Copy content Toggle raw display
\( T_{3}^{33} - 540 T_{3}^{31} + 148 T_{3}^{30} + 130392 T_{3}^{29} - 62370 T_{3}^{28} + \cdots + 50\!\cdots\!76 \) Copy content Toggle raw display