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Properties

Label 529.4.a.m
Level $529$
Weight $4$
Character orbit 529.a
Self dual yes
Analytic conductor $31.212$
Analytic rank $1$
Dimension $25$
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] = [529,4,Mod(1,529)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(529, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("529.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 529 = 23^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 529.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: \(31.2120103930\)
Analytic rank: \(1\)
Dimension: \(25\)
Twist minimal: no (minimal twist has level 23)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19} - 578 q^{20} - 352 q^{21} - 155 q^{22} + 803 q^{24} + 90 q^{25} - 850 q^{26} + 368 q^{27} - 459 q^{28} + 175 q^{29} - 893 q^{30} + 287 q^{31} + 164 q^{32} - 1020 q^{33} - 335 q^{34} + 462 q^{35} - 1092 q^{36} - 471 q^{37} - 810 q^{38} - 822 q^{39} - 1405 q^{40} - 73 q^{41} - 556 q^{42} - 901 q^{43} - 2073 q^{44} - 1384 q^{45} + 1452 q^{47} - 4028 q^{48} - 1092 q^{49} + 364 q^{50} - 2214 q^{51} + 1287 q^{52} - 2071 q^{53} + 2052 q^{54} + 1006 q^{55} - 4879 q^{56} - 418 q^{57} + 2796 q^{58} - 2713 q^{59} - 2805 q^{60} - 1225 q^{61} - 2852 q^{62} - 4003 q^{63} + 217 q^{64} - 2030 q^{65} - 2933 q^{66} - 767 q^{67} - 4175 q^{68} + 4851 q^{70} - 1683 q^{71} - 5265 q^{72} + 2203 q^{73} - 3089 q^{74} + 2333 q^{75} - 5252 q^{76} + 2760 q^{77} - 692 q^{78} - 5425 q^{79} - 4689 q^{80} + 1929 q^{81} - 2725 q^{82} - 5425 q^{83} - 4317 q^{84} - 912 q^{85} - 4359 q^{86} - 4404 q^{87} - 2610 q^{88} - 4933 q^{89} - 2695 q^{90} - 3619 q^{91} + 6375 q^{93} - 5117 q^{94} - 1338 q^{95} + 20 q^{96} - 2085 q^{97} + 5951 q^{98} - 7317 q^{99}+O(q^{100}) \) 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 −5.34818 −4.97765 20.6030 −16.6747 26.6214 7.69394 −67.4034 −2.22303 89.1791
1.2 −5.07272 −8.78974 17.7325 5.97134 44.5879 21.9327 −49.3704 50.2595 −30.2909
1.3 −4.35590 −1.21507 10.9738 6.90715 5.29273 −2.81570 −12.9537 −25.5236 −30.0868
1.4 −3.85347 −8.54515 6.84927 13.3372 32.9285 −17.3261 4.43432 46.0195 −51.3945
1.5 −3.80933 7.34288 6.51100 5.81014 −27.9715 −15.8241 5.67208 26.9179 −22.1327
1.6 −3.66204 2.67124 5.41053 4.26056 −9.78218 14.5832 9.48276 −19.8645 −15.6023
1.7 −3.19041 1.55052 2.17871 −19.2991 −4.94680 19.8587 18.5723 −24.5959 61.5722
1.8 −2.46235 2.34669 −1.93685 7.40267 −5.77838 −12.1855 24.4680 −21.4930 −18.2279
1.9 −2.15026 9.55258 −3.37638 −17.5072 −20.5405 3.15231 24.4622 64.2518 37.6451
1.10 −1.48270 −6.79236 −5.80160 −11.4888 10.0710 −21.1377 20.4636 19.1361 17.0345
1.11 −0.741592 −1.75597 −7.45004 −4.00517 1.30221 2.72150 11.4576 −23.9166 2.97020
1.12 −0.525953 5.51332 −7.72337 13.2745 −2.89975 −8.04220 8.26975 3.39674 −6.98174
1.13 −0.198677 −8.81112 −7.96053 −10.0672 1.75056 −25.3475 3.17098 50.6358 2.00012
1.14 0.929572 0.505183 −7.13590 10.4946 0.469604 30.2596 −14.0699 −26.7448 9.75547
1.15 0.976043 −6.99573 −7.04734 −1.89650 −6.82813 11.4459 −14.6869 21.9402 −1.85107
1.16 1.17387 9.69393 −6.62203 −0.587346 11.3794 −24.4606 −17.1643 66.9723 −0.689467
1.17 2.27917 −5.45949 −2.80539 −0.946196 −12.4431 13.4796 −24.6273 2.80604 −2.15654
1.18 2.45344 7.08198 −1.98063 −6.77342 17.3752 9.04270 −24.4869 23.1545 −16.6182
1.19 2.60332 −3.42880 −1.22274 15.6832 −8.92624 5.94573 −24.0097 −15.2434 40.8282
1.20 3.60724 7.96546 5.01217 −17.8878 28.7333 −17.9996 −10.7778 36.4486 −64.5257
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

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

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 529.4.a.m 25
23.b odd 2 1 529.4.a.n 25
23.d odd 22 2 23.4.c.a ✓ 50
69.g even 22 2 207.4.i.a 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.4.c.a ✓ 50 23.d odd 22 2
207.4.i.a 50 69.g even 22 2
529.4.a.m 25 1.a even 1 1 trivial
529.4.a.n 25 23.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(529))\):

\( T_{2}^{25} - 140 T_{2}^{23} - T_{2}^{22} + 8482 T_{2}^{21} + 88 T_{2}^{20} - 292209 T_{2}^{19} + \cdots + 1319713792 \) Copy content Toggle raw display
\( T_{3}^{25} + T_{3}^{24} - 420 T_{3}^{23} - 525 T_{3}^{22} + 75139 T_{3}^{21} + 108861 T_{3}^{20} + \cdots - 628808799728627 \) Copy content Toggle raw display
\( T_{5}^{25} + 51 T_{5}^{24} - 307 T_{5}^{23} - 52254 T_{5}^{22} - 329303 T_{5}^{21} + \cdots + 36\!\cdots\!71 \) Copy content Toggle raw display