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Properties

Label 1911.4.a.bf
Level $1911$
Weight $4$
Character orbit 1911.a
Self dual yes
Analytic conductor $112.753$
Analytic rank $0$
Dimension $22$
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] = [1911,4,Mod(1,1911)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1911, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1911.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.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: \(112.752650021\)
Analytic rank: \(0\)
Dimension: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + 2 q^{2} - 66 q^{3} + 114 q^{4} - 36 q^{5} - 6 q^{6} + 66 q^{8} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + 2 q^{2} - 66 q^{3} + 114 q^{4} - 36 q^{5} - 6 q^{6} + 66 q^{8} + 198 q^{9} - 48 q^{10} + 108 q^{11} - 342 q^{12} - 286 q^{13} + 108 q^{15} + 462 q^{16} + 18 q^{18} - 408 q^{19} - 416 q^{20} + 188 q^{22} + 304 q^{23} - 198 q^{24} + 882 q^{25} - 26 q^{26} - 594 q^{27} + 216 q^{29} + 144 q^{30} - 316 q^{31} + 770 q^{32} - 324 q^{33} - 776 q^{34} + 1026 q^{36} + 840 q^{37} + 436 q^{38} + 858 q^{39} - 40 q^{40} - 396 q^{41} + 768 q^{43} + 864 q^{44} - 324 q^{45} + 1380 q^{46} + 444 q^{47} - 1386 q^{48} + 70 q^{50} - 1482 q^{52} + 2612 q^{53} - 54 q^{54} - 1292 q^{55} + 1224 q^{57} + 1484 q^{58} - 1140 q^{59} + 1248 q^{60} + 392 q^{61} + 236 q^{62} + 2182 q^{64} + 468 q^{65} - 564 q^{66} + 2348 q^{67} + 3160 q^{68} - 912 q^{69} + 1624 q^{71} + 594 q^{72} - 1944 q^{73} + 3060 q^{74} - 2646 q^{75} - 2768 q^{76} + 78 q^{78} + 1904 q^{79} - 3820 q^{80} + 1782 q^{81} - 1360 q^{82} - 984 q^{83} + 1304 q^{85} + 2000 q^{86} - 648 q^{87} + 2164 q^{88} - 560 q^{89} - 432 q^{90} + 2608 q^{92} + 948 q^{93} - 1052 q^{94} + 2448 q^{95} - 2310 q^{96} - 2344 q^{97} + 972 q^{99}+O(q^{100}) \) 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 −5.20066 −3.00000 19.0469 5.39170 15.6020 0 −57.4511 9.00000 −28.0404
1.2 −5.12876 −3.00000 18.3042 −18.9181 15.3863 0 −52.8479 9.00000 97.0266
1.3 −4.62214 −3.00000 13.3642 14.2334 13.8664 0 −24.7941 9.00000 −65.7889
1.4 −4.44675 −3.00000 11.7736 −10.2032 13.3403 0 −16.7803 9.00000 45.3712
1.5 −3.73495 −3.00000 5.94985 1.27072 11.2048 0 7.65722 9.00000 −4.74606
1.6 −3.55984 −3.00000 4.67244 −14.9481 10.6795 0 11.8456 9.00000 53.2129
1.7 −2.63974 −3.00000 −1.03176 19.3247 7.91923 0 23.8415 9.00000 −51.0121
1.8 −2.43755 −3.00000 −2.05836 11.9028 7.31264 0 24.5177 9.00000 −29.0137
1.9 −1.34705 −3.00000 −6.18545 −15.3173 4.04115 0 19.1085 9.00000 20.6332
1.10 −0.870296 −3.00000 −7.24258 −15.8860 2.61089 0 13.2656 9.00000 13.8255
1.11 −0.600641 −3.00000 −7.63923 9.45906 1.80192 0 9.39357 9.00000 −5.68150
1.12 0.313253 −3.00000 −7.90187 2.91447 −0.939760 0 −4.98132 9.00000 0.912967
1.13 0.573013 −3.00000 −7.67166 −7.53489 −1.71904 0 −8.98006 9.00000 −4.31759
1.14 2.32382 −3.00000 −2.59985 5.78795 −6.97147 0 −24.6322 9.00000 13.4502
1.15 2.87018 −3.00000 0.237957 −0.689853 −8.61055 0 −22.2785 9.00000 −1.98000
1.16 2.97961 −3.00000 0.878068 −14.9505 −8.93883 0 −21.2206 9.00000 −44.5465
1.17 3.40858 −3.00000 3.61841 21.1668 −10.2257 0 −14.9350 9.00000 72.1486
1.18 3.68266 −3.00000 5.56198 −10.3138 −11.0480 0 −8.97840 9.00000 −37.9821
1.19 4.69758 −3.00000 14.0673 −17.7035 −14.0928 0 28.5016 9.00000 −83.1639
1.20 4.84404 −3.00000 15.4647 9.89189 −14.5321 0 36.1595 9.00000 47.9167
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(7\) \(1\)
\(13\) \(1\)

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 1911.4.a.bf ✓ 22
7.b odd 2 1 1911.4.a.bg yes 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1911.4.a.bf ✓ 22 1.a even 1 1 trivial
1911.4.a.bg yes 22 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1911))\):

\( T_{2}^{22} - 2 T_{2}^{21} - 143 T_{2}^{20} + 256 T_{2}^{19} + 8785 T_{2}^{18} - 13858 T_{2}^{17} + \cdots - 998164352 \) Copy content Toggle raw display
\( T_{5}^{22} + 36 T_{5}^{21} - 1168 T_{5}^{20} - 54092 T_{5}^{19} + 423628 T_{5}^{18} + \cdots - 80\!\cdots\!00 \) Copy content Toggle raw display