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Properties

Label 3023.2.a.c
Level $3023$
Weight $2$
Character orbit 3023.a
Self dual yes
Analytic conductor $24.139$
Analytic rank $0$
Dimension $149$
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] = [3023,2,Mod(1,3023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3023, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3023 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3023.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: \(24.1387765310\)
Analytic rank: \(0\)
Dimension: \(149\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 149 q + 13 q^{2} + 16 q^{3} + 169 q^{4} + 15 q^{5} + 15 q^{6} + 59 q^{7} + 36 q^{8} + 189 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 149 q + 13 q^{2} + 16 q^{3} + 169 q^{4} + 15 q^{5} + 15 q^{6} + 59 q^{7} + 36 q^{8} + 189 q^{9} + 16 q^{10} + 17 q^{11} + 40 q^{12} + 65 q^{13} + 4 q^{14} + 19 q^{15} + 205 q^{16} + 55 q^{17} + 60 q^{18} + 33 q^{19} + 23 q^{20} + 30 q^{21} + 78 q^{22} + 31 q^{23} + 36 q^{24} + 280 q^{25} - 7 q^{26} + 52 q^{27} + 165 q^{28} + 34 q^{29} + 17 q^{30} + 30 q^{31} + 65 q^{32} + 86 q^{33} + 37 q^{34} + 12 q^{35} + 210 q^{36} + 138 q^{37} + 15 q^{38} + 37 q^{39} + 27 q^{40} + 57 q^{41} + 2 q^{42} + 92 q^{43} + 37 q^{44} + 50 q^{45} + 62 q^{46} + 26 q^{47} + 79 q^{48} + 266 q^{49} + 19 q^{50} + 28 q^{51} + 139 q^{52} + 44 q^{53} + 33 q^{54} + 36 q^{55} - 2 q^{56} + 207 q^{57} + 150 q^{58} + 13 q^{59} - 15 q^{60} + 87 q^{61} + 22 q^{62} + 161 q^{63} + 254 q^{64} + 137 q^{65} - 25 q^{66} + 87 q^{67} + 68 q^{68} - 16 q^{69} + 28 q^{70} + 32 q^{71} + 120 q^{72} + 329 q^{73} + 29 q^{74} + 37 q^{75} + 42 q^{76} + 45 q^{77} + 63 q^{79} - 17 q^{80} + 269 q^{81} + 29 q^{82} + 51 q^{83} + 6 q^{84} + 224 q^{85} - 20 q^{86} + 34 q^{87} + 199 q^{88} + 24 q^{89} - 103 q^{90} + 46 q^{91} + 22 q^{92} + 119 q^{93} + 18 q^{94} + 13 q^{95} - 6 q^{96} + 204 q^{97} - 22 q^{98} + 43 q^{99}+O(q^{100}) \) 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 −2.79982 1.64876 5.83901 4.08786 −4.61625 3.65264 −10.7486 −0.281576 −11.4453
1.2 −2.75643 −2.72709 5.59788 −0.973267 7.51701 3.36408 −9.91730 4.43700 2.68274
1.3 −2.73700 1.09976 5.49117 −1.78720 −3.01004 −0.117357 −9.55535 −1.79053 4.89156
1.4 −2.72970 3.00690 5.45128 −1.89429 −8.20795 4.89619 −9.42097 6.04146 5.17085
1.5 −2.72126 −1.39359 5.40527 −0.252051 3.79234 2.55578 −9.26665 −1.05789 0.685898
1.6 −2.66851 −1.65721 5.12093 3.05483 4.42226 −3.04991 −8.32822 −0.253670 −8.15185
1.7 −2.59518 1.34644 4.73493 −3.04653 −3.49424 0.954367 −7.09763 −1.18711 7.90627
1.8 −2.58074 −0.0219044 4.66020 1.72579 0.0565296 −4.05085 −6.86527 −2.99952 −4.45380
1.9 −2.56504 −0.840581 4.57943 −2.93126 2.15612 −0.483402 −6.61633 −2.29342 7.51880
1.10 −2.54866 2.58366 4.49565 1.10400 −6.58485 0.238705 −6.36055 3.67528 −2.81371
1.11 −2.53692 1.87715 4.43599 3.26757 −4.76219 0.468866 −6.17992 0.523699 −8.28957
1.12 −2.47928 0.378092 4.14684 −3.89417 −0.937396 4.71932 −5.32264 −2.85705 9.65476
1.13 −2.47463 −1.65586 4.12377 −3.95862 4.09762 −1.75311 −5.25554 −0.258142 9.79610
1.14 −2.38355 −2.90233 3.68133 3.78839 6.91786 4.93550 −4.00753 5.42352 −9.02982
1.15 −2.36128 3.07942 3.57562 −3.46068 −7.27136 −2.28140 −3.72048 6.48282 8.17163
1.16 −2.26207 −2.94089 3.11696 −3.83807 6.65251 2.91999 −2.52665 5.64886 8.68198
1.17 −2.25206 −2.13369 3.07177 2.22465 4.80519 4.53091 −2.41368 1.55263 −5.01003
1.18 −2.24293 0.188028 3.03073 0.454947 −0.421733 3.69452 −2.31186 −2.96465 −1.02041
1.19 −2.22541 −2.71692 2.95244 1.78055 6.04625 −0.468418 −2.11958 4.38164 −3.96246
1.20 −2.22083 0.538465 2.93210 2.14893 −1.19584 −3.02689 −2.07005 −2.71006 −4.77242
See next 80 embeddings (of 149 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.149
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3023\) \(-1\)

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 3023.2.a.c ✓ 149
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3023.2.a.c ✓ 149 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{149} - 13 T_{2}^{148} - 149 T_{2}^{147} + 2640 T_{2}^{146} + 8499 T_{2}^{145} + \cdots + 11448901199699 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3023))\). Copy content Toggle raw display