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Properties

Label 3023.2.a.b
Level $3023$
Weight $2$
Character orbit 3023.a
Self dual yes
Analytic conductor $24.139$
Analytic rank $1$
Dimension $102$
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: \(1\)
Dimension: \(102\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 102 q - 11 q^{2} - 16 q^{3} + 83 q^{4} - 17 q^{5} - 17 q^{6} - 53 q^{7} - 36 q^{8} + 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 102 q - 11 q^{2} - 16 q^{3} + 83 q^{4} - 17 q^{5} - 17 q^{6} - 53 q^{7} - 36 q^{8} + 64 q^{9} - 22 q^{10} - 26 q^{11} - 40 q^{12} - 57 q^{13} - 4 q^{14} - 25 q^{15} + 49 q^{16} - 51 q^{17} - 44 q^{18} - 29 q^{19} - 23 q^{20} - 34 q^{21} - 67 q^{22} - 15 q^{23} - 36 q^{24} - 17 q^{25} - 19 q^{26} - 52 q^{27} - 139 q^{28} - 39 q^{29} - 31 q^{30} - 47 q^{31} - 63 q^{32} - 74 q^{33} - 27 q^{34} - 28 q^{35} + 16 q^{36} - 123 q^{37} + 5 q^{38} - 31 q^{39} - 63 q^{40} - 49 q^{41} - 14 q^{42} - 85 q^{43} - 24 q^{44} - 46 q^{45} - 76 q^{46} - 8 q^{47} - 49 q^{48} + q^{49} - 29 q^{50} - 16 q^{51} - 117 q^{52} - 40 q^{53} - 23 q^{54} - 50 q^{55} + 22 q^{56} - 177 q^{57} - 117 q^{58} + 9 q^{59} - 51 q^{60} - 98 q^{61} - 29 q^{62} - 95 q^{63} - 2 q^{64} - 87 q^{65} + 35 q^{66} - 81 q^{67} - 48 q^{68} - 16 q^{69} - 28 q^{70} - 28 q^{71} - 96 q^{72} - 281 q^{73} + 6 q^{74} - 19 q^{75} - 72 q^{76} - 59 q^{77} - 40 q^{78} - 62 q^{79} - 27 q^{80} - 42 q^{81} - 71 q^{82} - 37 q^{83} - 10 q^{84} - 176 q^{85} - 15 q^{86} - 14 q^{87} - 194 q^{88} - 42 q^{89} - 49 q^{90} - 26 q^{91} - 44 q^{92} - 113 q^{93} - 44 q^{94} - 43 q^{95} - 62 q^{96} - 165 q^{97} - 54 q^{98} - 36 q^{99}+O(q^{100}) \) 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 −2.82218 1.44696 5.96470 −2.42863 −4.08359 −3.87388 −11.1891 −0.906299 6.85402
1.2 −2.67341 −1.93118 5.14712 3.14238 5.16283 −0.0937788 −8.41354 0.729453 −8.40088
1.3 −2.65830 −2.90963 5.06657 0.328791 7.73468 −4.63379 −8.15186 5.46595 −0.874026
1.4 −2.65630 0.441342 5.05593 1.50622 −1.17234 2.23285 −8.11746 −2.80522 −4.00098
1.5 −2.62270 3.16443 4.87855 0.281063 −8.29934 −1.96968 −7.54958 7.01359 −0.737145
1.6 −2.58272 −1.36417 4.67044 −2.30954 3.52327 −3.25317 −6.89699 −1.13904 5.96490
1.7 −2.55695 2.05472 4.53801 3.17707 −5.25383 −4.72966 −6.48956 1.22189 −8.12363
1.8 −2.51803 −3.11630 4.34047 −1.75300 7.84693 −0.280410 −5.89336 6.71133 4.41411
1.9 −2.51182 −0.260451 4.30922 0.100193 0.654206 2.81849 −5.80034 −2.93217 −0.251665
1.10 −2.40834 1.83936 3.80012 1.01099 −4.42981 −0.892143 −4.33531 0.383243 −2.43482
1.11 −2.37249 −2.70742 3.62871 −0.313727 6.42334 0.839528 −3.86409 4.33014 0.744313
1.12 −2.31861 1.97777 3.37595 −0.388470 −4.58568 0.999986 −3.19029 0.911573 0.900709
1.13 −2.27849 −0.768464 3.19153 3.90009 1.75094 −0.690650 −2.71490 −2.40946 −8.88633
1.14 −2.26874 −0.453119 3.14719 −1.07194 1.02801 −3.34690 −2.60269 −2.79468 2.43195
1.15 −2.19290 1.86690 2.80881 −3.00215 −4.09393 0.996597 −1.77365 0.485320 6.58341
1.16 −2.16677 −0.886183 2.69489 2.15742 1.92015 −0.109518 −1.50566 −2.21468 −4.67462
1.17 −2.07705 1.06042 2.31413 −3.26145 −2.20255 −3.80613 −0.652458 −1.87551 6.77419
1.18 −2.05260 1.71432 2.21315 0.204688 −3.51881 2.36216 −0.437508 −0.0610937 −0.420142
1.19 −2.04188 −1.14969 2.16926 −1.47080 2.34753 4.14397 −0.345607 −1.67820 3.00319
1.20 −1.93187 −2.43632 1.73210 3.31734 4.70665 −3.42652 0.517541 2.93568 −6.40866
See next 80 embeddings (of 102 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.102
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.b ✓ 102
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
3023.2.a.b ✓ 102 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{102} + 11 T_{2}^{101} - 83 T_{2}^{100} - 1330 T_{2}^{99} + 2177 T_{2}^{98} + 76919 T_{2}^{97} + \cdots - 2003 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3023))\). Copy content Toggle raw display