↑

Properties

Label 451.4.a.c
Level $451$
Weight $4$
Character orbit 451.a
Self dual yes
Analytic conductor $26.610$
Analytic rank $0$
Dimension $27$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(27\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 27 q + 4 q^{2} + 11 q^{3} + 140 q^{4} + 47 q^{5} - 38 q^{7} + 66 q^{8} + 330 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 27 q + 4 q^{2} + 11 q^{3} + 140 q^{4} + 47 q^{5} - 38 q^{7} + 66 q^{8} + 330 q^{9} - 70 q^{10} - 297 q^{11} + 390 q^{12} + 124 q^{13} + 203 q^{14} + 402 q^{15} + 684 q^{16} + 140 q^{17} + 41 q^{18} + 7 q^{19} + 877 q^{20} + 292 q^{21} - 44 q^{22} + 266 q^{23} - 52 q^{24} + 948 q^{25} + 971 q^{26} + 602 q^{27} - 12 q^{28} + 969 q^{29} + 1022 q^{30} + 154 q^{31} + 437 q^{32} - 121 q^{33} + 750 q^{34} + 819 q^{35} + 2378 q^{36} + 69 q^{37} - 25 q^{38} - 316 q^{39} + 213 q^{40} - 1107 q^{41} - 35 q^{42} + 175 q^{43} - 1540 q^{44} + 1411 q^{45} - 1112 q^{46} + 1438 q^{47} + 2821 q^{48} + 2861 q^{49} + 258 q^{50} + 988 q^{51} + 947 q^{52} + 2589 q^{53} + 307 q^{54} - 517 q^{55} + 1901 q^{56} + 702 q^{57} + 812 q^{58} + 1531 q^{59} + 4604 q^{60} - 489 q^{61} + 1553 q^{62} - 1943 q^{63} + 2420 q^{64} + 4474 q^{65} + 845 q^{67} + 257 q^{68} + 6764 q^{69} - 1050 q^{70} + 4822 q^{71} + 562 q^{72} + 362 q^{73} + 449 q^{74} + 817 q^{75} - 1255 q^{76} + 418 q^{77} + 1525 q^{78} - 2443 q^{79} + 10436 q^{80} + 9103 q^{81} - 164 q^{82} + 425 q^{83} + 6750 q^{84} + 2671 q^{85} + 838 q^{86} + 2846 q^{87} - 726 q^{88} + 4810 q^{89} - 6001 q^{90} - 526 q^{91} + 1278 q^{92} + 4327 q^{93} + 2916 q^{94} + 2583 q^{95} - 1620 q^{96} + 908 q^{97} + 186 q^{98} - 3630 q^{99}+O(q^{100}) \) 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 −5.35296 9.10779 20.6542 16.8640 −48.7537 28.3525 −67.7376 55.9518 −90.2722
1.2 −5.22267 −0.357672 19.2763 17.1215 1.86800 −25.2329 −58.8923 −26.8721 −89.4197
1.3 −5.19225 0.276245 18.9595 −5.50330 −1.43433 −2.60110 −56.9045 −26.9237 28.5745
1.4 −4.13053 −1.06215 9.06128 −1.11592 4.38724 13.2668 −4.38364 −25.8718 4.60932
1.5 −4.11446 −9.74505 8.92877 6.99193 40.0956 −29.0642 −3.82137 67.9661 −28.7680
1.6 −4.00755 10.0945 8.06045 −11.3468 −40.4541 −22.4541 −0.242264 74.8985 45.4730
1.7 −3.19332 −6.92835 2.19730 −12.3630 22.1244 9.46447 18.5299 21.0020 39.4789
1.8 −3.02382 6.77475 1.14346 21.2118 −20.4856 −8.94310 20.7329 18.8973 −64.1405
1.9 −2.77538 3.94027 −0.297289 −13.4591 −10.9357 −24.3839 23.0281 −11.4743 37.3541
1.10 −1.72970 −2.76920 −5.00814 2.91385 4.78988 −16.0526 22.5002 −19.3316 −5.04009
1.11 −1.53160 3.92515 −5.65420 5.54212 −6.01176 25.1379 20.9128 −11.5932 −8.48832
1.12 −1.23767 −9.13202 −6.46818 17.9540 11.3024 18.5861 17.9068 56.3939 −22.2211
1.13 −0.0502520 −5.52622 −7.99747 −0.512032 0.277704 35.3008 0.803905 3.53916 0.0257306
1.14 0.365927 2.59839 −7.86610 −17.8143 0.950821 −19.2464 −5.80583 −20.2484 −6.51873
1.15 1.12672 9.54949 −6.73050 5.29467 10.7596 16.4724 −16.5972 64.1927 5.96561
1.16 1.25213 −5.41491 −6.43216 4.50122 −6.78019 −30.9019 −18.0710 2.32122 5.63614
1.17 1.33637 1.89144 −6.21411 14.1273 2.52766 −20.3271 −18.9953 −23.4225 18.8793
1.18 1.79662 −1.46938 −4.77215 −10.6779 −2.63993 −2.21358 −22.9467 −24.8409 −19.1843
1.19 2.82934 −4.16022 0.00514928 −18.3540 −11.7707 5.51054 −22.6201 −9.69258 −51.9297
1.20 3.56816 5.34431 4.73177 18.0720 19.0694 24.2740 −11.6616 1.56166 64.4839
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
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.c ✓ 27
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
451.4.a.c ✓ 27 1.a even 1 1 trivial