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Properties

Label 723.4.a.b
Level $723$
Weight $4$
Character orbit 723.a
Self dual yes
Analytic conductor $42.658$
Analytic rank $0$
Dimension $29$
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] = [723,4,Mod(1,723)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(723, 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("723.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 723 = 3 \cdot 241 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 723.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: \(42.6583809342\)
Analytic rank: \(0\)
Dimension: \(29\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 29 q + 9 q^{2} - 87 q^{3} + 97 q^{4} + 62 q^{5} - 27 q^{6} - 30 q^{7} + 108 q^{8} + 261 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 29 q + 9 q^{2} - 87 q^{3} + 97 q^{4} + 62 q^{5} - 27 q^{6} - 30 q^{7} + 108 q^{8} + 261 q^{9} + 51 q^{10} + 46 q^{11} - 291 q^{12} + 250 q^{13} + 84 q^{14} - 186 q^{15} + 333 q^{16} + 128 q^{17} + 81 q^{18} + 58 q^{19} + 405 q^{20} + 90 q^{21} - 48 q^{22} + 232 q^{23} - 324 q^{24} + 707 q^{25} + 238 q^{26} - 783 q^{27} - 89 q^{28} + 590 q^{29} - 153 q^{30} - 468 q^{31} + 1068 q^{32} - 138 q^{33} + 287 q^{34} + 474 q^{35} + 873 q^{36} + 842 q^{37} + 160 q^{38} - 750 q^{39} + 434 q^{40} + 814 q^{41} - 252 q^{42} + 20 q^{43} + 150 q^{44} + 558 q^{45} - 37 q^{46} + 1004 q^{47} - 999 q^{48} + 1239 q^{49} + 839 q^{50} - 384 q^{51} + 1928 q^{52} + 2192 q^{53} - 243 q^{54} + 432 q^{55} + 437 q^{56} - 174 q^{57} - 28 q^{58} + 1288 q^{59} - 1215 q^{60} + 1502 q^{61} + 3059 q^{62} - 270 q^{63} + 3372 q^{64} + 2312 q^{65} + 144 q^{66} + 358 q^{67} + 4990 q^{68} - 696 q^{69} + 5366 q^{70} + 1938 q^{71} + 972 q^{72} + 3266 q^{73} + 2510 q^{74} - 2121 q^{75} + 3591 q^{76} + 5098 q^{77} - 714 q^{78} - 292 q^{79} + 8235 q^{80} + 2349 q^{81} + 4511 q^{82} + 4256 q^{83} + 267 q^{84} + 1998 q^{85} + 6860 q^{86} - 1770 q^{87} + 5935 q^{88} + 6428 q^{89} + 459 q^{90} - 1650 q^{91} + 6823 q^{92} + 1404 q^{93} + 3025 q^{94} + 1802 q^{95} - 3204 q^{96} + 5040 q^{97} + 9410 q^{98} + 414 q^{99}+O(q^{100}) \) 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 −5.12899 −3.00000 18.3065 15.2554 15.3870 8.97213 −52.8621 9.00000 −78.2447
1.2 −4.65163 −3.00000 13.6376 −2.92252 13.9549 10.4866 −26.2242 9.00000 13.5945
1.3 −4.62178 −3.00000 13.3609 −11.1805 13.8654 −17.2413 −24.7769 9.00000 51.6737
1.4 −4.61401 −3.00000 13.2891 17.5076 13.8420 −13.8232 −24.4039 9.00000 −80.7804
1.5 −3.78227 −3.00000 6.30557 −5.68778 11.3468 −15.9387 6.40879 9.00000 21.5127
1.6 −3.38796 −3.00000 3.47828 −5.05017 10.1639 −1.36724 15.3194 9.00000 17.1098
1.7 −2.69232 −3.00000 −0.751438 −17.4306 8.07695 16.5096 23.5616 9.00000 46.9288
1.8 −2.14536 −3.00000 −3.39743 15.4086 6.43608 −11.8098 24.4516 9.00000 −33.0569
1.9 −1.83966 −3.00000 −4.61566 −1.96073 5.51898 −1.07670 23.2085 9.00000 3.60708
1.10 −1.68847 −3.00000 −5.14906 22.1888 5.06541 −11.1315 22.2018 9.00000 −37.4651
1.11 −1.68254 −3.00000 −5.16907 2.08567 5.04761 30.8603 22.1574 9.00000 −3.50922
1.12 −1.28359 −3.00000 −6.35240 0.508995 3.85077 −35.7971 18.4226 9.00000 −0.653341
1.13 −1.16445 −3.00000 −6.64406 −10.5306 3.49334 9.63072 17.0522 9.00000 12.2623
1.14 −0.364523 −3.00000 −7.86712 5.79603 1.09357 11.9832 5.78393 9.00000 −2.11279
1.15 1.12035 −3.00000 −6.74482 13.1582 −3.36105 29.4550 −16.5193 9.00000 14.7417
1.16 1.14345 −3.00000 −6.69252 −0.465287 −3.43036 −21.2063 −16.8002 9.00000 −0.532033
1.17 1.17966 −3.00000 −6.60840 −5.20729 −3.53898 19.7482 −17.2329 9.00000 −6.14283
1.18 1.18901 −3.00000 −6.58626 19.7501 −3.56703 −30.4473 −17.3432 9.00000 23.4831
1.19 2.61315 −3.00000 −1.17143 −6.42911 −7.83946 15.9906 −23.9664 9.00000 −16.8002
1.20 2.75926 −3.00000 −0.386494 −13.3161 −8.27777 −12.5857 −23.1405 9.00000 −36.7427
See all 29 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.29
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(241\) \(1\)

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 723.4.a.b ✓ 29
3.b odd 2 1 2169.4.a.c 29
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
723.4.a.b ✓ 29 1.a even 1 1 trivial
2169.4.a.c 29 3.b odd 2 1