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Properties

Label 451.4.a.d
Level $451$
Weight $4$
Character orbit 451.a
Self dual yes
Analytic conductor $26.610$
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] = [451,4,Mod(1,451)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(451, 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("451.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 451 = 11 \cdot 41 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 451.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: \(26.6098614126\)
Analytic rank: \(0\)
Dimension: \(29\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 29 q + 10 q^{2} + 3 q^{3} + 132 q^{4} + 49 q^{5} + 36 q^{6} + 60 q^{7} + 102 q^{8} + 374 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 29 q + 10 q^{2} + 3 q^{3} + 132 q^{4} + 49 q^{5} + 36 q^{6} + 60 q^{7} + 102 q^{8} + 374 q^{9} + 70 q^{10} + 319 q^{11} - 128 q^{12} + 62 q^{13} + 263 q^{14} - 112 q^{15} + 636 q^{16} + 232 q^{17} + 521 q^{18} + 149 q^{19} - 7 q^{20} + 380 q^{21} + 110 q^{22} + 204 q^{23} + 40 q^{24} + 1124 q^{25} + 49 q^{26} + 12 q^{27} + 772 q^{28} + 1253 q^{29} - 216 q^{30} + 40 q^{31} + 641 q^{32} + 33 q^{33} - 2 q^{34} + 817 q^{35} + 2298 q^{36} + 71 q^{37} + 839 q^{38} + 1160 q^{39} + 123 q^{40} + 1189 q^{41} + 133 q^{42} + 431 q^{43} + 1452 q^{44} + 1907 q^{45} + 1584 q^{46} + 124 q^{47} - 893 q^{48} + 1651 q^{49} + 3276 q^{50} + 680 q^{51} + 915 q^{52} + 2033 q^{53} + 1073 q^{54} + 539 q^{55} + 3389 q^{56} + 2594 q^{57} - 32 q^{58} + 1029 q^{59} - 2780 q^{60} + 3287 q^{61} + 549 q^{62} + 1477 q^{63} + 4688 q^{64} - 138 q^{65} + 396 q^{66} + 189 q^{67} + 1747 q^{68} - 902 q^{69} + 1044 q^{70} + 1754 q^{71} + 6504 q^{72} + 1374 q^{73} + 2895 q^{74} + 335 q^{75} + 1027 q^{76} + 660 q^{77} + 2469 q^{78} + 3613 q^{79} - 1644 q^{80} + 2481 q^{81} + 410 q^{82} + 1165 q^{83} + 88 q^{84} + 3989 q^{85} + 6742 q^{86} - 610 q^{87} + 1122 q^{88} + 1336 q^{89} + 5671 q^{90} + 1394 q^{91} + 2882 q^{92} + 1191 q^{93} + 1868 q^{94} + 2461 q^{95} + 9302 q^{96} + 326 q^{97} + 9400 q^{98} + 4114 q^{99}+O(q^{100}) \) 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 −5.60984 −6.80981 23.4703 1.54971 38.2019 −14.6036 −86.7857 19.3736 −8.69361
1.2 −4.95330 0.876581 16.5352 17.2757 −4.34197 10.9337 −42.2772 −26.2316 −85.5718
1.3 −4.52909 5.58124 12.5126 −21.4075 −25.2779 −5.13502 −20.4381 4.15024 96.9565
1.4 −4.44132 6.52786 11.7253 1.69483 −28.9923 10.0385 −16.5453 15.6130 −7.52727
1.5 −4.30184 −2.80916 10.5058 −7.46491 12.0846 −16.1764 −10.7796 −19.1086 32.1128
1.6 −3.57754 −8.37009 4.79880 −6.42952 29.9443 16.8434 11.4524 43.0583 23.0019
1.7 −2.72907 9.66935 −0.552152 9.40259 −26.3884 3.65977 23.3395 66.4964 −25.6604
1.8 −2.54982 −7.10581 −1.49842 2.11689 18.1185 27.9622 24.2193 23.4925 −5.39768
1.9 −2.42354 0.802356 −2.12644 −8.54551 −1.94454 10.8788 24.5419 −26.3562 20.7104
1.10 −2.26217 −3.21007 −2.88258 19.0307 7.26173 −26.0514 24.6183 −16.6954 −43.0507
1.11 −1.67288 −10.2113 −5.20146 6.59327 17.0823 −9.72561 22.0845 77.2703 −11.0298
1.12 −0.913225 1.88443 −7.16602 7.13713 −1.72091 −24.6752 13.8500 −23.4489 −6.51781
1.13 −0.775334 6.24489 −7.39886 15.4866 −4.84188 32.8794 11.9393 11.9986 −12.0073
1.14 0.0633683 8.33069 −7.99598 −10.7072 0.527902 −19.4259 −1.01364 42.4004 −0.678499
1.15 0.708047 −0.341601 −7.49867 −14.0013 −0.241870 −29.0786 −10.9738 −26.8833 −9.91358
1.16 1.33280 −0.343069 −6.22365 11.1133 −0.457241 6.50295 −18.9572 −26.8823 14.8118
1.17 1.59418 −5.19012 −5.45858 14.4729 −8.27400 21.9938 −21.4554 −0.0626172 23.0724
1.18 1.74605 4.73454 −4.95130 −16.6398 8.26676 32.1451 −22.6136 −4.58411 −29.0540
1.19 2.30193 −5.89141 −2.70113 −11.5702 −13.5616 0.814820 −24.6332 7.70870 −26.6337
1.20 2.56740 7.65100 −1.40845 21.5396 19.6432 −4.42893 −24.1553 31.5378 55.3007
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
\(11\) \( -1 \)
\(41\) \( -1 \)

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 451.4.a.d ✓ 29
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
451.4.a.d ✓ 29 1.a even 1 1 trivial