↑

Properties

Label 1502.4.a.c
Level $1502$
Weight $4$
Character orbit 1502.a
Self dual yes
Analytic conductor $88.621$
Analytic rank $0$
Dimension $50$
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: \(0\)
Dimension: \(50\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 50 q - 100 q^{2} + 16 q^{3} + 200 q^{4} + 11 q^{5} - 32 q^{6} + 82 q^{7} - 400 q^{8} + 520 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 50 q - 100 q^{2} + 16 q^{3} + 200 q^{4} + 11 q^{5} - 32 q^{6} + 82 q^{7} - 400 q^{8} + 520 q^{9} - 22 q^{10} - 113 q^{11} + 64 q^{12} + 280 q^{13} - 164 q^{14} + 149 q^{15} + 800 q^{16} + 206 q^{17} - 1040 q^{18} + 167 q^{19} + 44 q^{20} + 34 q^{21} + 226 q^{22} + 55 q^{23} - 128 q^{24} + 1495 q^{25} - 560 q^{26} + 556 q^{27} + 328 q^{28} - 21 q^{29} - 298 q^{30} + 883 q^{31} - 1600 q^{32} + 928 q^{33} - 412 q^{34} - 477 q^{35} + 2080 q^{36} + 1668 q^{37} - 334 q^{38} - 254 q^{39} - 88 q^{40} + 578 q^{41} - 68 q^{42} + 781 q^{43} - 452 q^{44} + 632 q^{45} - 110 q^{46} + 207 q^{47} + 256 q^{48} + 3354 q^{49} - 2990 q^{50} + 639 q^{51} + 1120 q^{52} + 344 q^{53} - 1112 q^{54} + 1483 q^{55} - 656 q^{56} + 1427 q^{57} + 42 q^{58} - 349 q^{59} + 596 q^{60} + 119 q^{61} - 1766 q^{62} + 1487 q^{63} + 3200 q^{64} + 1811 q^{65} - 1856 q^{66} + 2546 q^{67} + 824 q^{68} + 524 q^{69} + 954 q^{70} - 292 q^{71} - 4160 q^{72} + 4502 q^{73} - 3336 q^{74} + 1203 q^{75} + 668 q^{76} + 1279 q^{77} + 508 q^{78} + 839 q^{79} + 176 q^{80} + 7354 q^{81} - 1156 q^{82} - 539 q^{83} + 136 q^{84} + 2640 q^{85} - 1562 q^{86} + 1281 q^{87} + 904 q^{88} + 1451 q^{89} - 1264 q^{90} + 3997 q^{91} + 220 q^{92} + 4948 q^{93} - 414 q^{94} - 2864 q^{95} - 512 q^{96} + 7585 q^{97} - 6708 q^{98} - 2410 q^{99}+O(q^{100}) \) 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 −9.64515 4.00000 −17.6721 19.2903 13.9621 −8.00000 66.0289 35.3442
1.2 −2.00000 −9.59429 4.00000 15.5056 19.1886 10.1319 −8.00000 65.0504 −31.0112
1.3 −2.00000 −9.40572 4.00000 9.65316 18.8114 −11.0514 −8.00000 61.4676 −19.3063
1.4 −2.00000 −8.36978 4.00000 −6.70437 16.7396 −12.8029 −8.00000 43.0532 13.4087
1.5 −2.00000 −8.16529 4.00000 −1.86828 16.3306 −22.0940 −8.00000 39.6719 3.73655
1.6 −2.00000 −7.61846 4.00000 −21.5141 15.2369 6.54668 −8.00000 31.0409 43.0283
1.7 −2.00000 −7.56481 4.00000 −13.8274 15.1296 −18.2002 −8.00000 30.2264 27.6549
1.8 −2.00000 −7.28893 4.00000 18.5942 14.5779 26.5868 −8.00000 26.1285 −37.1883
1.9 −2.00000 −6.83728 4.00000 19.3533 13.6746 −28.9038 −8.00000 19.7484 −38.7066
1.10 −2.00000 −6.74081 4.00000 4.55841 13.4816 2.39100 −8.00000 18.4385 −9.11683
1.11 −2.00000 −6.65183 4.00000 5.90777 13.3037 34.5897 −8.00000 17.2468 −11.8155
1.12 −2.00000 −5.97873 4.00000 −4.86312 11.9575 7.19611 −8.00000 8.74522 9.72623
1.13 −2.00000 −5.26714 4.00000 7.05284 10.5343 16.2931 −8.00000 0.742754 −14.1057
1.14 −2.00000 −4.62416 4.00000 −16.9152 9.24832 −6.35676 −8.00000 −5.61716 33.8304
1.15 −2.00000 −4.60042 4.00000 −11.8069 9.20085 31.4184 −8.00000 −5.83610 23.6138
1.16 −2.00000 −4.02059 4.00000 5.63898 8.04117 −3.56225 −8.00000 −10.8349 −11.2780
1.17 −2.00000 −3.79236 4.00000 −13.0979 7.58471 27.6803 −8.00000 −12.6180 26.1958
1.18 −2.00000 −2.48842 4.00000 −0.779603 4.97683 −32.8216 −8.00000 −20.8078 1.55921
1.19 −2.00000 −2.08855 4.00000 12.8128 4.17711 33.3668 −8.00000 −22.6379 −25.6255
1.20 −2.00000 −1.77526 4.00000 3.05878 3.55052 −14.9284 −8.00000 −23.8485 −6.11756
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.50
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.c ✓ 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1502.4.a.c ✓ 50 1.a even 1 1 trivial