↑

Properties

Label 2107.4.a.h
Level $2107$
Weight $4$
Character orbit 2107.a
Self dual yes
Analytic conductor $124.317$
Analytic rank $1$
Dimension $30$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2107,4,Mod(1,2107)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2107, 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("2107.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2107 = 7^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2107.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: \(124.317024382\)
Analytic rank: \(1\)
Dimension: \(30\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 8 q^{2} + 100 q^{4} - 90 q^{8} + 264 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q - 8 q^{2} + 100 q^{4} - 90 q^{8} + 264 q^{9} - 60 q^{11} - 96 q^{15} + 372 q^{16} - 1008 q^{18} - 234 q^{22} - 214 q^{23} + 520 q^{25} - 870 q^{29} - 12 q^{30} - 1548 q^{32} + 1142 q^{36} - 1246 q^{37} - 416 q^{39} - 1290 q^{43} - 446 q^{44} - 660 q^{46} - 278 q^{50} - 3702 q^{51} - 2960 q^{53} + 620 q^{57} - 3634 q^{58} - 898 q^{60} + 2578 q^{64} - 4848 q^{65} + 928 q^{67} - 1708 q^{71} - 7900 q^{72} + 1714 q^{74} - 138 q^{78} - 3562 q^{79} + 2210 q^{81} - 948 q^{85} + 344 q^{86} + 2502 q^{88} - 3848 q^{92} - 11986 q^{93} - 2894 q^{95} - 2804 q^{99}+O(q^{100}) \) 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 −5.54060 −7.57873 22.6982 −6.01458 41.9907 0 −81.4370 30.4371 33.3244
1.2 −5.54060 7.57873 22.6982 6.01458 −41.9907 0 −81.4370 30.4371 −33.3244
1.3 −4.85099 −8.32225 15.5321 11.9330 40.3712 0 −36.5381 42.2599 −57.8867
1.4 −4.85099 8.32225 15.5321 −11.9330 −40.3712 0 −36.5381 42.2599 57.8867
1.5 −3.80243 −6.75863 6.45848 −12.6768 25.6992 0 5.86153 18.6791 48.2025
1.6 −3.80243 6.75863 6.45848 12.6768 −25.6992 0 5.86153 18.6791 −48.2025
1.7 −3.73014 −2.48917 5.91395 −6.92907 9.28495 0 7.78127 −20.8040 25.8464
1.8 −3.73014 2.48917 5.91395 6.92907 −9.28495 0 7.78127 −20.8040 −25.8464
1.9 −2.49169 −1.67643 −1.79146 22.2435 4.17716 0 24.3973 −24.1896 −55.4240
1.10 −2.49169 1.67643 −1.79146 −22.2435 −4.17716 0 24.3973 −24.1896 55.4240
1.11 −1.93072 −10.2626 −4.27231 8.49116 19.8142 0 23.6944 78.3210 −16.3941
1.12 −1.93072 10.2626 −4.27231 −8.49116 −19.8142 0 23.6944 78.3210 16.3941
1.13 −1.63380 −3.59773 −5.33070 −10.5338 5.87797 0 21.7797 −14.0564 17.2102
1.14 −1.63380 3.59773 −5.33070 10.5338 −5.87797 0 21.7797 −14.0564 −17.2102
1.15 −0.195345 −6.09602 −7.96184 11.7846 1.19083 0 3.11806 10.1615 −2.30205
1.16 −0.195345 6.09602 −7.96184 −11.7846 −1.19083 0 3.11806 10.1615 2.30205
1.17 0.740371 −9.08049 −7.45185 −1.06386 −6.72294 0 −11.4401 55.4554 −0.787653
1.18 0.740371 9.08049 −7.45185 1.06386 6.72294 0 −11.4401 55.4554 0.787653
1.19 1.13382 −0.406652 −6.71446 −9.12555 −0.461069 0 −16.6835 −26.8346 −10.3467
1.20 1.13382 0.406652 −6.71446 9.12555 0.461069 0 −16.6835 −26.8346 10.3467
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(43\) \(1\)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2107.4.a.h ✓ 30
7.b odd 2 1 inner 2107.4.a.h ✓ 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2107.4.a.h ✓ 30 1.a even 1 1 trivial
2107.4.a.h ✓ 30 7.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2107))\):

\( T_{2}^{15} + 4 T_{2}^{14} - 77 T_{2}^{13} - 293 T_{2}^{12} + 2262 T_{2}^{11} + 8147 T_{2}^{10} + \cdots - 245568 \) Copy content Toggle raw display
\( T_{3}^{30} - 537 T_{3}^{28} + 127351 T_{3}^{26} - 17620538 T_{3}^{24} + 1582505521 T_{3}^{22} + \cdots - 79\!\cdots\!52 \) Copy content Toggle raw display