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Properties

Label 1573.4.a.p
Level $1573$
Weight $4$
Character orbit 1573.a
Self dual yes
Analytic conductor $92.810$
Analytic rank $1$
Dimension $34$
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] = [1573,4,Mod(1,1573)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1573, 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("1573.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1573 = 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1573.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: \(92.8100044390\)
Analytic rank: \(1\)
Dimension: \(34\)
Twist minimal: no (minimal twist has level 143)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q + 3 q^{2} - 29 q^{3} + 97 q^{4} - 28 q^{5} - 36 q^{6} + 36 q^{7} + 57 q^{8} + 265 q^{9} + 18 q^{10} - 262 q^{12} - 442 q^{13} - 231 q^{14} - 196 q^{15} + 225 q^{16} + 209 q^{17} + 190 q^{18} + 107 q^{19} - 211 q^{20} + 68 q^{21} - 632 q^{23} - 152 q^{24} + 296 q^{25} - 39 q^{26} - 920 q^{27} + 931 q^{28} + 32 q^{29} + 300 q^{30} - 290 q^{31} - 876 q^{32} - 602 q^{34} - 104 q^{35} - 611 q^{36} - 656 q^{37} - 1361 q^{38} + 377 q^{39} - 1159 q^{40} + 1121 q^{41} + 79 q^{42} - 349 q^{43} - 1024 q^{45} - 490 q^{46} - 1608 q^{47} - 1827 q^{48} + 808 q^{49} + 1322 q^{50} - 1414 q^{51} - 1261 q^{52} - 2608 q^{53} - 3131 q^{54} - 1675 q^{56} + 2150 q^{57} - 1673 q^{58} - 2011 q^{59} - 201 q^{60} + 236 q^{61} - 1396 q^{62} - 1206 q^{63} + 1331 q^{64} + 364 q^{65} - 3213 q^{67} + 1321 q^{68} - 162 q^{69} + 174 q^{70} - 3756 q^{71} + 5074 q^{72} - 823 q^{73} - 2550 q^{74} - 3063 q^{75} - 2004 q^{76} + 468 q^{78} + 2120 q^{79} - 5005 q^{80} + 710 q^{81} - 2534 q^{82} + 3843 q^{83} - 7191 q^{84} - 1582 q^{85} - 3542 q^{86} - 962 q^{87} - 3633 q^{89} + 995 q^{90} - 468 q^{91} - 2072 q^{92} - 508 q^{93} + 6309 q^{94} - 1916 q^{95} + 2150 q^{96} + 1195 q^{97} + 1487 q^{98}+O(q^{100}) \) 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 −5.47680 −5.23580 21.9954 2.19924 28.6755 25.7545 −76.6500 0.413622 −12.0448
1.2 −5.35278 0.409649 20.6523 −12.3131 −2.19276 3.32229 −67.7249 −26.8322 65.9093
1.3 −4.30134 −2.16661 10.5016 10.8931 9.31934 −4.30816 −10.7601 −22.3058 −46.8550
1.4 −4.28885 2.44568 10.3942 9.58602 −10.4891 23.5443 −10.2684 −21.0187 −41.1130
1.5 −4.13806 −5.83637 9.12355 −0.336615 24.1513 −10.5216 −4.64934 7.06321 1.39293
1.6 −3.72684 8.55098 5.88935 −11.5420 −31.8681 11.8343 7.86604 46.1192 43.0152
1.7 −3.03846 3.05634 1.23221 −7.70730 −9.28656 −31.1628 20.5636 −17.6588 23.4183
1.8 −3.03663 7.63811 1.22110 −1.65564 −23.1941 −1.44786 20.5850 31.3407 5.02756
1.9 −2.76431 −9.14077 −0.358601 −4.24890 25.2679 16.4872 23.1057 56.5536 11.7453
1.10 −2.41223 3.79234 −2.18115 17.1876 −9.14801 7.32188 24.5593 −12.6181 −41.4606
1.11 −2.38105 −6.39431 −2.33061 −5.31428 15.2252 −5.31409 24.5977 13.8872 12.6535
1.12 −2.17354 −7.10694 −3.27573 −16.1248 15.4472 35.4995 24.5082 23.5086 35.0478
1.13 −1.75570 −9.39742 −4.91751 17.7296 16.4991 −19.1621 22.6793 61.3115 −31.1279
1.14 −1.14032 −1.98038 −6.69966 4.19108 2.25828 2.88584 16.7624 −23.0781 −4.77919
1.15 −0.772290 8.82957 −7.40357 −17.1506 −6.81899 −3.36156 11.8960 50.9614 13.2452
1.16 −0.495149 0.728931 −7.75483 −20.6600 −0.360929 8.57647 7.80099 −26.4687 10.2298
1.17 −0.305925 −0.688798 −7.90641 −14.6552 0.210720 −34.1750 4.86616 −26.5256 4.48337
1.18 −0.0313827 5.72009 −7.99902 7.55527 −0.179512 6.19881 0.502093 5.71940 −0.237105
1.19 0.568087 6.42425 −7.67728 4.18544 3.64954 32.4879 −8.90606 14.2710 2.37769
1.20 1.21343 −0.584783 −6.52760 21.2304 −0.709592 −13.2251 −17.6282 −26.6580 25.7616
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(11\) \(-1\)
\(13\) \(1\)

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 1573.4.a.p 34
11.b odd 2 1 1573.4.a.o 34
11.d odd 10 2 143.4.h.a ✓ 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.h.a ✓ 68 11.d odd 10 2
1573.4.a.o 34 11.b odd 2 1
1573.4.a.p 34 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{34} - 3 T_{2}^{33} - 180 T_{2}^{32} + 514 T_{2}^{31} + 14572 T_{2}^{30} - 39135 T_{2}^{29} + \cdots + 165041029120 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1573))\). Copy content Toggle raw display