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Properties

Label 1805.2.b.k
Level $1805$
Weight $2$
Character orbit 1805.b
Analytic conductor $14.413$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 18 q^{4} - 3 q^{5} - 12 q^{6} - 12 q^{9} - 6 q^{10} + 12 q^{11} - 24 q^{14} - 9 q^{15} + 6 q^{16} + 21 q^{20} + 6 q^{21} + 42 q^{24} - 3 q^{25} - 12 q^{26} - 36 q^{29} - 18 q^{30} + 42 q^{31} - 6 q^{34} + 27 q^{35} - 6 q^{36} - 24 q^{39} + 12 q^{40} + 60 q^{41} + 30 q^{44} + 9 q^{45} + 6 q^{46} - 12 q^{49} + 18 q^{50} + 30 q^{51} + 24 q^{54} + 33 q^{55} + 18 q^{56} - 60 q^{59} - 42 q^{60} + 30 q^{61} + 18 q^{65} + 36 q^{66} - 66 q^{69} + 9 q^{70} + 96 q^{71} - 24 q^{74} + 36 q^{75} - 72 q^{79} - 42 q^{80} - 96 q^{81} + 54 q^{84} - 27 q^{85} + 108 q^{86} - 84 q^{89} - 93 q^{90} + 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1084.1 − 2.68669i − 2.14658i −5.21828 −1.71227 − 1.43810i −5.76720 − 2.78303i 8.64651i −1.60782 −3.86371 + 4.60034i
1084.2 − 2.37097i − 2.28512i −3.62149 1.17411 + 1.90301i −5.41794 1.63677i 3.84450i −2.22176 4.51198 − 2.78378i
1084.3 − 2.32462i 1.14858i −3.40387 −2.01201 − 0.975617i 2.67001 0.143302i 3.26348i 1.68077 −2.26794 + 4.67716i
1084.4 − 1.96177i 0.187708i −1.84854 1.81111 − 1.31144i 0.368240 − 0.677067i − 0.297123i 2.96477 −2.57274 − 3.55299i
1084.5 − 1.78468i 2.38377i −1.18508 −1.16534 + 1.90840i 4.25426 − 4.23911i − 1.45438i −2.68235 3.40588 + 2.07976i
1084.6 − 1.61907i 1.18857i −0.621387 0.326390 − 2.21212i 1.92438 2.23190i − 2.23207i 1.58730 −3.58157 − 0.528448i
1084.7 − 1.47917i − 2.48321i −0.187941 0.111989 + 2.23326i −3.67308 − 3.24988i − 2.68034i −3.16631 3.30337 − 0.165651i
1084.8 − 1.22159i 0.804421i 0.507728 −2.23387 − 0.0991400i 0.982669 3.79180i − 3.06341i 2.35291 −0.121108 + 2.72886i
1084.9 − 1.04740i − 0.531453i 0.902948 1.65192 − 1.50704i −0.556645 − 2.74033i − 3.04056i 2.71756 −1.57847 − 1.73023i
1084.10 − 0.449373i − 1.95684i 1.79806 1.87757 − 1.21438i −0.879352 − 2.06079i − 1.70675i −0.829224 −0.545709 − 0.843732i
1084.11 − 0.249751i − 2.30156i 1.93762 −2.08007 − 0.820550i −0.574816 3.96043i − 0.983424i −2.29718 −0.204933 + 0.519499i
1084.12 − 0.244477i 2.73837i 1.94023 0.750459 + 2.10637i 0.669469 − 1.94027i − 0.963297i −4.49866 0.514961 − 0.183470i
1084.13 0.244477i − 2.73837i 1.94023 0.750459 − 2.10637i 0.669469 1.94027i 0.963297i −4.49866 0.514961 + 0.183470i
1084.14 0.249751i 2.30156i 1.93762 −2.08007 + 0.820550i −0.574816 − 3.96043i 0.983424i −2.29718 −0.204933 − 0.519499i
1084.15 0.449373i 1.95684i 1.79806 1.87757 + 1.21438i −0.879352 2.06079i 1.70675i −0.829224 −0.545709 + 0.843732i
1084.16 1.04740i 0.531453i 0.902948 1.65192 + 1.50704i −0.556645 2.74033i 3.04056i 2.71756 −1.57847 + 1.73023i
1084.17 1.22159i − 0.804421i 0.507728 −2.23387 + 0.0991400i 0.982669 − 3.79180i 3.06341i 2.35291 −0.121108 − 2.72886i
1084.18 1.47917i 2.48321i −0.187941 0.111989 − 2.23326i −3.67308 3.24988i 2.68034i −3.16631 3.30337 + 0.165651i
1084.19 1.61907i − 1.18857i −0.621387 0.326390 + 2.21212i 1.92438 − 2.23190i 2.23207i 1.58730 −3.58157 + 0.528448i
1084.20 1.78468i − 2.38377i −1.18508 −1.16534 − 1.90840i 4.25426 4.23911i 1.45438i −2.68235 3.40588 − 2.07976i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1084.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1805.2.b.k 24
5.b even 2 1 inner 1805.2.b.k 24
5.c odd 4 2 9025.2.a.cu 24
19.b odd 2 1 1805.2.b.l 24
19.e even 9 2 95.2.p.a ✓ 48
57.l odd 18 2 855.2.da.b 48
95.d odd 2 1 1805.2.b.l 24
95.g even 4 2 9025.2.a.ct 24
95.p even 18 2 95.2.p.a ✓ 48
95.q odd 36 4 475.2.l.f 48
285.bd odd 18 2 855.2.da.b 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.2.p.a ✓ 48 19.e even 9 2
95.2.p.a ✓ 48 95.p even 18 2
475.2.l.f 48 95.q odd 36 4
855.2.da.b 48 57.l odd 18 2
855.2.da.b 48 285.bd odd 18 2
1805.2.b.k 24 1.a even 1 1 trivial
1805.2.b.k 24 5.b even 2 1 inner
1805.2.b.l 24 19.b odd 2 1
1805.2.b.l 24 95.d odd 2 1
9025.2.a.ct 24 95.g even 4 2
9025.2.a.cu 24 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1805, [\chi])\):

\( T_{2}^{24} + 33 T_{2}^{22} + 468 T_{2}^{20} + 3743 T_{2}^{18} + 18618 T_{2}^{16} + 59871 T_{2}^{14} + \cdots + 19 \) Copy content Toggle raw display
\( T_{29}^{12} + 18 T_{29}^{11} + 45 T_{29}^{10} - 756 T_{29}^{9} - 3600 T_{29}^{8} + 9369 T_{29}^{7} + \cdots - 263169 \) Copy content Toggle raw display