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Properties

Label 451.4.a.b
Level $451$
Weight $4$
Character orbit 451.a
Self dual yes
Analytic conductor $26.610$
Analytic rank $1$
Dimension $23$
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: \(1\)
Dimension: \(23\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 23 q - 8 q^{2} - 9 q^{3} + 72 q^{4} - 51 q^{5} - 48 q^{6} - 80 q^{7} - 114 q^{8} + 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 23 q - 8 q^{2} - 9 q^{3} + 72 q^{4} - 51 q^{5} - 48 q^{6} - 80 q^{7} - 114 q^{8} + 104 q^{9} - 70 q^{10} + 253 q^{11} + 134 q^{12} - 114 q^{13} - 45 q^{14} - 32 q^{15} + 108 q^{16} - 176 q^{17} - 37 q^{18} - 371 q^{19} - 51 q^{20} - 388 q^{21} - 88 q^{22} - 178 q^{23} - 628 q^{24} + 374 q^{25} - 257 q^{26} - 420 q^{27} - 516 q^{28} - 1299 q^{29} - 646 q^{30} - 314 q^{31} - 1195 q^{32} - 99 q^{33} - 254 q^{34} - 773 q^{35} - 402 q^{36} - 637 q^{37} - 225 q^{38} - 1492 q^{39} - 1557 q^{40} - 943 q^{41} - 763 q^{42} - 915 q^{43} + 792 q^{44} - 889 q^{45} - 970 q^{46} + 306 q^{47} + 325 q^{48} + 973 q^{49} + 126 q^{50} - 776 q^{51} - 419 q^{52} - 2461 q^{53} - 1905 q^{54} - 561 q^{55} - 907 q^{56} + 154 q^{57} - 344 q^{58} + 363 q^{59} - 780 q^{60} - 983 q^{61} + 145 q^{62} - 2481 q^{63} - 832 q^{64} - 1830 q^{65} - 528 q^{66} - 1411 q^{67} - 3441 q^{68} - 274 q^{69} - 390 q^{70} - 416 q^{71} - 192 q^{72} + 710 q^{73} - 4333 q^{74} - 2853 q^{75} - 5851 q^{76} - 880 q^{77} - 4171 q^{78} - 4541 q^{79} - 1996 q^{80} - 2757 q^{81} + 328 q^{82} - 2985 q^{83} - 5144 q^{84} - 2505 q^{85} - 1462 q^{86} - 1126 q^{87} - 1254 q^{88} - 4252 q^{89} - 3011 q^{90} + 1254 q^{91} - 3898 q^{92} - 2949 q^{93} + 642 q^{94} - 2525 q^{95} - 3546 q^{96} + 98 q^{97} - 2870 q^{98} + 1144 q^{99}+O(q^{100}) \) 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 −5.43866 5.73546 21.5790 0.134471 −31.1932 −15.4603 −73.8514 5.89551 −0.731341
1.2 −5.21260 −0.357037 19.1712 −10.2337 1.86109 34.3084 −58.2308 −26.8725 53.3441
1.3 −4.63030 8.26212 13.4396 9.65091 −38.2561 −25.1146 −25.1872 41.2627 −44.6866
1.4 −4.50998 −6.94961 12.3399 14.2574 31.3426 −8.19774 −19.5731 21.2970 −64.3004
1.5 −4.13481 −3.92998 9.09669 −7.74273 16.2497 −10.1685 −4.53461 −11.5553 32.0147
1.6 −3.51850 0.774854 4.37987 13.9299 −2.72633 22.6551 12.7374 −26.3996 −49.0123
1.7 −2.97271 3.63635 0.837010 −16.3126 −10.8098 −10.4810 21.2935 −13.7769 48.4926
1.8 −2.28183 3.99780 −2.79327 6.80824 −9.12228 −14.3837 24.6284 −11.0176 −15.5352
1.9 −2.20686 −7.71494 −3.12979 −18.4174 17.0258 −34.2044 24.5618 32.5204 40.6446
1.10 −1.27557 8.46739 −6.37292 −13.8238 −10.8008 12.5770 18.3337 44.6967 17.6332
1.11 −0.670195 −2.46677 −7.55084 −3.36360 1.65322 17.3753 10.4221 −20.9151 2.25427
1.12 −0.565161 −6.73462 −7.68059 1.56450 3.80614 −17.3609 8.86207 18.3551 −0.884196
1.13 −0.306934 −6.54132 −7.90579 −21.8699 2.00775 17.1883 4.88203 15.7888 6.71260
1.14 0.646240 −6.79829 −7.58237 15.6854 −4.39333 −4.67089 −10.0700 19.2167 10.1366
1.15 1.15411 3.41157 −6.66803 0.510938 3.93733 12.4610 −16.9285 −15.3612 0.589679
1.16 1.71576 4.55426 −5.05615 2.06137 7.81404 −11.4462 −22.4013 −6.25871 3.53683
1.17 2.86005 −9.45065 0.179862 −4.53549 −27.0293 26.0003 −22.3660 62.3148 −12.9717
1.18 2.92526 7.86888 0.557174 −7.30396 23.0185 −29.5472 −21.7722 34.9192 −21.3660
1.19 3.20749 −0.315208 2.28797 19.4927 −1.01102 −31.4832 −18.3213 −26.9006 62.5225
1.20 3.81234 −1.99776 6.53394 3.33214 −7.61614 0.0722030 −5.58911 −23.0090 12.7032
See all 23 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.23
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.b ✓ 23
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
451.4.a.b ✓ 23 1.a even 1 1 trivial