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Properties

Label 2873.2.a.z
Level $2873$
Weight $2$
Character orbit 2873.a
Self dual yes
Analytic conductor $22.941$
Analytic rank $0$
Dimension $24$
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] = [2873,2,Mod(1,2873)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2873, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2873.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2873 = 13^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2873.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: \(22.9410205007\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 5 q^{2} + q^{3} + 25 q^{4} + 11 q^{5} + 5 q^{6} + 33 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 5 q^{2} + q^{3} + 25 q^{4} + 11 q^{5} + 5 q^{6} + 33 q^{7} + 6 q^{8} + 29 q^{9} - 7 q^{10} + 22 q^{11} + q^{12} - 18 q^{14} + 29 q^{15} + 27 q^{16} + 24 q^{17} + 18 q^{18} + 20 q^{19} + 7 q^{20} - 4 q^{21} + 7 q^{22} - q^{23} + 13 q^{24} + 35 q^{25} - 11 q^{27} + 54 q^{28} + 9 q^{29} - 22 q^{30} + 67 q^{31} + 2 q^{32} + 11 q^{33} + 5 q^{34} + 18 q^{35} + 22 q^{36} + 47 q^{37} + 12 q^{38} - 61 q^{40} + 24 q^{41} + 24 q^{42} - 35 q^{43} + 44 q^{44} - 6 q^{45} + 6 q^{46} + 26 q^{47} - 7 q^{48} + 51 q^{49} + 6 q^{50} + q^{51} + 2 q^{53} - 18 q^{54} + 7 q^{55} - 34 q^{56} + 35 q^{57} + 75 q^{58} + 5 q^{59} + 41 q^{60} + 8 q^{61} + 29 q^{62} + 90 q^{63} + 58 q^{64} - 156 q^{66} + 77 q^{67} + 25 q^{68} - 60 q^{69} + 19 q^{70} + 66 q^{71} + 21 q^{72} + 37 q^{73} + 10 q^{74} + 8 q^{75} + 3 q^{76} + 28 q^{77} + 7 q^{79} + 8 q^{80} + 4 q^{82} + 12 q^{83} - 4 q^{84} + 11 q^{85} + 15 q^{86} + 19 q^{87} - 17 q^{88} - 35 q^{89} + 22 q^{90} - 117 q^{92} + 9 q^{93} - 8 q^{94} - 88 q^{95} + 120 q^{96} + 43 q^{97} - 38 q^{98} + 72 q^{99}+O(q^{100}) \) 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 −2.67825 −2.27272 5.17301 0.833086 6.08691 3.93190 −8.49809 2.16527 −2.23121
1.2 −2.63455 0.456063 4.94084 2.32680 −1.20152 3.33576 −7.74780 −2.79201 −6.13007
1.3 −2.13253 2.65759 2.54767 3.14543 −5.66739 4.14404 −1.16791 4.06281 −6.70771
1.4 −2.00551 1.01585 2.02208 0.146557 −2.03730 1.10126 −0.0442872 −1.96805 −0.293923
1.5 −1.81467 −2.15950 1.29304 −2.71933 3.91879 3.75697 1.28290 1.66345 4.93470
1.6 −1.36752 −2.08674 −0.129896 0.220301 2.85365 −2.93976 2.91267 1.35449 −0.301266
1.7 −1.15956 2.62321 −0.655417 2.43355 −3.04178 −1.00673 3.07912 3.88125 −2.82185
1.8 −0.971429 1.27585 −1.05632 −2.95868 −1.23940 2.11860 2.96900 −1.37221 2.87415
1.9 −0.567809 −3.15503 −1.67759 −4.05966 1.79145 3.59152 2.08817 6.95418 2.30511
1.10 −0.546083 1.17298 −1.70179 3.07632 −0.640541 −2.98745 2.02149 −1.62413 −1.67993
1.11 −0.215338 −1.43588 −1.95363 3.78845 0.309200 4.72811 0.851366 −0.938239 −0.815797
1.12 0.0660340 −0.327789 −1.99564 0.468371 −0.0216452 1.39129 −0.263848 −2.89255 0.0309284
1.13 0.746998 −1.42111 −1.44199 3.76269 −1.06157 3.12469 −2.57116 −0.980436 2.81072
1.14 0.753456 2.73570 −1.43230 −2.41010 2.06123 5.26341 −2.58609 4.48407 −1.81590
1.15 1.29273 3.21172 −0.328841 1.87655 4.15190 0.932954 −3.01057 7.31515 2.42588
1.16 1.31344 0.425303 −0.274872 −3.50529 0.558610 −0.533081 −2.98791 −2.81912 −4.60400
1.17 1.40628 −2.89533 −0.0223681 1.22522 −4.07165 −0.00936402 −2.84402 5.38294 1.72300
1.18 1.43489 2.33667 0.0589148 3.18692 3.35288 −0.527416 −2.78525 2.46005 4.57289
1.19 1.82901 −2.04300 1.34526 −0.271875 −3.73665 −4.28757 −1.19752 1.17384 −0.497260
1.20 2.02053 0.582439 2.08253 4.34572 1.17683 2.56687 0.166750 −2.66076 8.78065
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(13\) \(1\)
\(17\) \(-1\)

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 2873.2.a.z yes 24
13.b even 2 1 2873.2.a.y ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2873.2.a.y ✓ 24 13.b even 2 1
2873.2.a.z yes 24 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2873))\):

\( T_{2}^{24} - 5 T_{2}^{23} - 24 T_{2}^{22} + 153 T_{2}^{21} + 187 T_{2}^{20} - 1957 T_{2}^{19} + \cdots - 113 \) Copy content Toggle raw display
\( T_{3}^{24} - T_{3}^{23} - 50 T_{3}^{22} + 52 T_{3}^{21} + 1075 T_{3}^{20} - 1161 T_{3}^{19} + \cdots - 17927 \) Copy content Toggle raw display
\( T_{5}^{24} - 11 T_{5}^{23} - 17 T_{5}^{22} + 591 T_{5}^{21} - 1092 T_{5}^{20} - 11892 T_{5}^{19} + \cdots - 853 \) Copy content Toggle raw display