↑

Properties

Label 1502.4.a.b
Level $1502$
Weight $4$
Character orbit 1502.a
Self dual yes
Analytic conductor $88.621$
Analytic rank $1$
Dimension $44$
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] = [1502,4,Mod(1,1502)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1502, 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("1502.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1502 = 2 \cdot 751 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1502.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: \(88.6208688286\)
Analytic rank: \(1\)
Dimension: \(44\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 44 q + 88 q^{2} - 44 q^{3} + 176 q^{4} - 53 q^{5} - 88 q^{6} - 142 q^{7} + 352 q^{8} + 326 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 44 q + 88 q^{2} - 44 q^{3} + 176 q^{4} - 53 q^{5} - 88 q^{6} - 142 q^{7} + 352 q^{8} + 326 q^{9} - 106 q^{10} - 203 q^{11} - 176 q^{12} - 334 q^{13} - 284 q^{14} - 221 q^{15} + 704 q^{16} - 272 q^{17} + 652 q^{18} - 503 q^{19} - 212 q^{20} - 404 q^{21} - 406 q^{22} - 553 q^{23} - 352 q^{24} + 605 q^{25} - 668 q^{26} - 1466 q^{27} - 568 q^{28} - 791 q^{29} - 442 q^{30} - 1457 q^{31} + 1408 q^{32} - 628 q^{33} - 544 q^{34} - 1271 q^{35} + 1304 q^{36} - 1706 q^{37} - 1006 q^{38} - 860 q^{39} - 424 q^{40} - 758 q^{41} - 808 q^{42} - 1461 q^{43} - 812 q^{44} - 1878 q^{45} - 1106 q^{46} - 1921 q^{47} - 704 q^{48} + 1596 q^{49} + 1210 q^{50} - 1577 q^{51} - 1336 q^{52} - 1014 q^{53} - 2932 q^{54} - 3033 q^{55} - 1136 q^{56} - 2047 q^{57} - 1582 q^{58} - 2437 q^{59} - 884 q^{60} - 2273 q^{61} - 2914 q^{62} - 4595 q^{63} + 2816 q^{64} - 1693 q^{65} - 1256 q^{66} - 3648 q^{67} - 1088 q^{68} - 4292 q^{69} - 2542 q^{70} - 4924 q^{71} + 2608 q^{72} - 5788 q^{73} - 3412 q^{74} - 6005 q^{75} - 2012 q^{76} - 3531 q^{77} - 1720 q^{78} - 3875 q^{79} - 848 q^{80} + 1612 q^{81} - 1516 q^{82} - 5625 q^{83} - 1616 q^{84} - 6344 q^{85} - 2922 q^{86} - 5515 q^{87} - 1624 q^{88} - 2077 q^{89} - 3756 q^{90} - 6171 q^{91} - 2212 q^{92} - 4794 q^{93} - 3842 q^{94} - 4688 q^{95} - 1408 q^{96} - 7027 q^{97} + 3192 q^{98} - 6488 q^{99}+O(q^{100}) \) 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 2.00000 −10.1263 4.00000 2.43062 −20.2525 −32.3181 8.00000 75.5412 4.86124
1.2 2.00000 −9.77964 4.00000 −13.0427 −19.5593 31.7288 8.00000 68.6413 −26.0853
1.3 2.00000 −9.38473 4.00000 21.7665 −18.7695 −26.4750 8.00000 61.0731 43.5330
1.4 2.00000 −9.07839 4.00000 2.21719 −18.1568 32.7596 8.00000 55.4171 4.43438
1.5 2.00000 −8.53688 4.00000 11.3722 −17.0738 3.99119 8.00000 45.8783 22.7445
1.6 2.00000 −8.39554 4.00000 9.98455 −16.7911 −9.51460 8.00000 43.4850 19.9691
1.7 2.00000 −8.15032 4.00000 −18.9098 −16.3006 −33.9405 8.00000 39.4278 −37.8196
1.8 2.00000 −7.89476 4.00000 −17.7174 −15.7895 −2.95702 8.00000 35.3272 −35.4347
1.9 2.00000 −7.74781 4.00000 10.5526 −15.4956 25.0232 8.00000 33.0285 21.1053
1.10 2.00000 −6.78301 4.00000 −15.8202 −13.5660 −21.5223 8.00000 19.0093 −31.6403
1.11 2.00000 −6.36909 4.00000 −16.4705 −12.7382 13.0587 8.00000 13.5653 −32.9411
1.12 2.00000 −5.48581 4.00000 −2.45046 −10.9716 16.2353 8.00000 3.09413 −4.90091
1.13 2.00000 −5.45113 4.00000 −9.90282 −10.9023 −30.0029 8.00000 2.71483 −19.8056
1.14 2.00000 −4.97550 4.00000 −2.30607 −9.95101 4.59058 8.00000 −2.24435 −4.61214
1.15 2.00000 −4.89884 4.00000 −5.41507 −9.79767 −16.7235 8.00000 −3.00139 −10.8301
1.16 2.00000 −4.32293 4.00000 13.5901 −8.64586 −21.2351 8.00000 −8.31228 27.1802
1.17 2.00000 −3.70832 4.00000 −1.14066 −7.41665 19.1556 8.00000 −13.2483 −2.28133
1.18 2.00000 −3.28550 4.00000 −0.371617 −6.57100 20.7730 8.00000 −16.2055 −0.743234
1.19 2.00000 −3.21491 4.00000 14.6195 −6.42982 −7.21910 8.00000 −16.6644 29.2390
1.20 2.00000 −2.54275 4.00000 10.5516 −5.08550 −0.986017 8.00000 −20.5344 21.1031
See all 44 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.44
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(751\) \(1\)

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 1502.4.a.b ✓ 44
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1502.4.a.b ✓ 44 1.a even 1 1 trivial