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Properties

Label 2001.4.a.g
Level $2001$
Weight $4$
Character orbit 2001.a
Self dual yes
Analytic conductor $118.063$
Analytic rank $0$
Dimension $43$
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] = [2001,4,Mod(1,2001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2001, 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("2001.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2001.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: \(118.062821921\)
Analytic rank: \(0\)
Dimension: \(43\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 43 q + 2 q^{2} + 129 q^{3} + 210 q^{4} + 25 q^{5} + 6 q^{6} + 106 q^{7} + 27 q^{8} + 387 q^{9} + 32 q^{10} + 109 q^{11} + 630 q^{12} + 235 q^{13} + 205 q^{14} + 75 q^{15} + 1190 q^{16} + 228 q^{17} + 18 q^{18} + 291 q^{19} + 407 q^{20} + 318 q^{21} + 808 q^{22} - 989 q^{23} + 81 q^{24} + 1656 q^{25} - 289 q^{26} + 1161 q^{27} + 1831 q^{28} + 1247 q^{29} + 96 q^{30} + 694 q^{31} + 88 q^{32} + 327 q^{33} + 1158 q^{34} - 43 q^{35} + 1890 q^{36} + 1167 q^{37} + 35 q^{38} + 705 q^{39} + 1117 q^{40} + 977 q^{41} + 615 q^{42} + 1361 q^{43} + 798 q^{44} + 225 q^{45} - 46 q^{46} + 684 q^{47} + 3570 q^{48} + 3417 q^{49} + 267 q^{50} + 684 q^{51} + 3054 q^{52} + 1344 q^{53} + 54 q^{54} + 1072 q^{55} + 1741 q^{56} + 873 q^{57} + 58 q^{58} - 313 q^{59} + 1221 q^{60} + 3162 q^{61} - 1010 q^{62} + 954 q^{63} + 8795 q^{64} + 370 q^{65} + 2424 q^{66} + 2699 q^{67} + 2799 q^{68} - 2967 q^{69} + 443 q^{70} + 2140 q^{71} + 243 q^{72} + 922 q^{73} + 2281 q^{74} + 4968 q^{75} + 2237 q^{76} + 879 q^{77} - 867 q^{78} + 5078 q^{79} + 5377 q^{80} + 3483 q^{81} + 1045 q^{82} + 2670 q^{83} + 5493 q^{84} - 1087 q^{85} + 3249 q^{86} + 3741 q^{87} + 8305 q^{88} + 1893 q^{89} + 288 q^{90} + 6847 q^{91} - 4830 q^{92} + 2082 q^{93} - 1128 q^{94} + 6973 q^{95} + 264 q^{96} + 3040 q^{97} + 2581 q^{98} + 981 q^{99}+O(q^{100}) \) 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 −5.63036 3.00000 23.7010 19.6321 −16.8911 21.5239 −88.4023 9.00000 −110.536
1.2 −5.36915 3.00000 20.8278 −18.6335 −16.1075 32.0297 −68.8744 9.00000 100.046
1.3 −5.27166 3.00000 19.7903 2.53750 −15.8150 −13.9736 −62.1547 9.00000 −13.3768
1.4 −5.20060 3.00000 19.0462 −17.0220 −15.6018 −4.11066 −57.4470 9.00000 88.5244
1.5 −4.96128 3.00000 16.6143 13.1987 −14.8838 −5.77543 −42.7380 9.00000 −65.4825
1.6 −4.52180 3.00000 12.4467 −3.06147 −13.5654 −3.50584 −20.1072 9.00000 13.8433
1.7 −4.33098 3.00000 10.7574 −2.85492 −12.9929 −31.5232 −11.9423 9.00000 12.3646
1.8 −4.04073 3.00000 8.32748 2.10792 −12.1222 36.7948 −1.32324 9.00000 −8.51754
1.9 −3.72031 3.00000 5.84072 16.7227 −11.1609 −7.86226 8.03319 9.00000 −62.2137
1.10 −3.57151 3.00000 4.75569 2.83635 −10.7145 0.106712 11.5871 9.00000 −10.1301
1.11 −3.39189 3.00000 3.50493 16.9223 −10.1757 14.5403 15.2468 9.00000 −57.3986
1.12 −3.19768 3.00000 2.22518 −9.92909 −9.59305 −24.5578 18.4660 9.00000 31.7501
1.13 −2.66698 3.00000 −0.887221 −1.27379 −8.00094 27.2395 23.7020 9.00000 3.39716
1.14 −2.57596 3.00000 −1.36445 −11.7761 −7.72787 −25.7958 24.1224 9.00000 30.3347
1.15 −2.30758 3.00000 −2.67509 −15.1398 −6.92273 18.0689 24.6336 9.00000 34.9363
1.16 −1.79433 3.00000 −4.78036 10.2571 −5.38300 −20.5322 22.9322 9.00000 −18.4046
1.17 −1.48802 3.00000 −5.78581 11.2202 −4.46405 −8.52768 20.5135 9.00000 −16.6959
1.18 −1.11018 3.00000 −6.76749 19.4168 −3.33055 25.4542 16.3946 9.00000 −21.5562
1.19 −0.880630 3.00000 −7.22449 −21.4645 −2.64189 20.6875 13.4071 9.00000 18.9023
1.20 −0.659999 3.00000 −7.56440 −13.3599 −1.98000 15.6970 10.2725 9.00000 8.81749
See all 43 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.43
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(23\) \(1\)
\(29\) \(-1\)

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 2001.4.a.g ✓ 43
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2001.4.a.g ✓ 43 1.a even 1 1 trivial