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Properties

Label 4334.2.a.e
Level $4334$
Weight $2$
Character orbit 4334.a
Self dual yes
Analytic conductor $34.607$
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] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, 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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 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 −1.00000 −3.29945 1.00000 −3.72842 3.29945 −3.54518 −1.00000 7.88640 3.72842
1.2 −1.00000 −3.08498 1.00000 1.01853 3.08498 −2.58850 −1.00000 6.51711 −1.01853
1.3 −1.00000 −3.05385 1.00000 3.30243 3.05385 4.28183 −1.00000 6.32597 −3.30243
1.4 −1.00000 −2.81176 1.00000 −2.87657 2.81176 −0.0915560 −1.00000 4.90602 2.87657
1.5 −1.00000 −2.34418 1.00000 −2.76933 2.34418 1.79797 −1.00000 2.49516 2.76933
1.6 −1.00000 −2.15745 1.00000 1.30451 2.15745 3.75589 −1.00000 1.65457 −1.30451
1.7 −1.00000 −2.03428 1.00000 3.12875 2.03428 −4.32049 −1.00000 1.13829 −3.12875
1.8 −1.00000 −1.47170 1.00000 3.58412 1.47170 −0.948099 −1.00000 −0.834090 −3.58412
1.9 −1.00000 −1.15892 1.00000 −2.65435 1.15892 4.05701 −1.00000 −1.65690 2.65435
1.10 −1.00000 −1.02498 1.00000 −1.91029 1.02498 0.691966 −1.00000 −1.94941 1.91029
1.11 −1.00000 −0.392540 1.00000 2.96246 0.392540 −1.89262 −1.00000 −2.84591 −2.96246
1.12 −1.00000 −0.257887 1.00000 0.105378 0.257887 −1.45976 −1.00000 −2.93349 −0.105378
1.13 −1.00000 0.0886475 1.00000 −3.04967 −0.0886475 −1.08307 −1.00000 −2.99214 3.04967
1.14 −1.00000 0.140715 1.00000 0.341585 −0.140715 −2.48538 −1.00000 −2.98020 −0.341585
1.15 −1.00000 0.626459 1.00000 −4.16763 −0.626459 4.47360 −1.00000 −2.60755 4.16763
1.16 −1.00000 0.745887 1.00000 2.52923 −0.745887 4.14909 −1.00000 −2.44365 −2.52923
1.17 −1.00000 1.08316 1.00000 −1.14511 −1.08316 2.88226 −1.00000 −1.82677 1.14511
1.18 −1.00000 1.21094 1.00000 −0.613687 −1.21094 −4.17411 −1.00000 −1.53363 0.613687
1.19 −1.00000 2.01603 1.00000 2.21808 −2.01603 1.91345 −1.00000 1.06437 −2.21808
1.20 −1.00000 2.05410 1.00000 4.08690 −2.05410 0.841598 −1.00000 1.21932 −4.08690
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
\(2\) \(1\)
\(11\) \(1\)
\(197\) \(-1\)

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 4334.2.a.e ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4334.2.a.e ✓ 24 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 4 T_{3}^{23} - 42 T_{3}^{22} - 175 T_{3}^{21} + 735 T_{3}^{20} + 3231 T_{3}^{19} - 6952 T_{3}^{18} - 32836 T_{3}^{17} + 38598 T_{3}^{16} + 201163 T_{3}^{15} - 128107 T_{3}^{14} - 766057 T_{3}^{13} + 249310 T_{3}^{12} + \cdots + 292 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4334))\). Copy content Toggle raw display