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Properties

Label 1573.4.a.o
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 −5.46923 −6.64067 21.9125 −12.5247 36.3193 −3.24336 −76.0904 17.0984 68.5006
1.2 −4.77325 4.58517 14.7839 −9.06658 −21.8862 11.8931 −32.3813 −5.97621 43.2770
1.3 −4.49806 −9.16217 12.2325 14.5583 41.2120 −13.8178 −19.0381 56.9454 −65.4843
1.4 −4.47881 4.48996 12.0598 4.91735 −20.1097 26.1499 −18.1829 −6.84022 −22.0239
1.5 −4.42253 2.24443 11.5588 −14.3858 −9.92609 −33.6112 −15.7390 −21.9625 63.6217
1.6 −4.41665 −3.92530 11.5068 13.0664 17.3366 6.68918 −15.4881 −11.5921 −57.7097
1.7 −4.35050 −0.852587 10.9269 4.75210 3.70918 −8.90050 −12.7333 −26.2731 −20.6740
1.8 −3.59997 −9.67368 4.95976 −16.9616 34.8249 15.3656 10.9448 66.5802 61.0612
1.9 −2.77160 7.63306 −0.318244 −4.52057 −21.1558 2.79283 23.0548 31.2637 12.5292
1.10 −2.74116 6.45484 −0.486036 6.42298 −17.6937 11.8479 23.2616 14.6649 −17.6064
1.11 −2.33608 −4.49638 −2.54272 12.7804 10.5039 −34.2639 24.6287 −6.78256 −29.8560
1.12 −2.02870 −4.53812 −3.88438 −12.2012 9.20648 12.3738 24.1098 −6.40548 24.7525
1.13 −1.60161 −4.88610 −5.43484 −3.91984 7.82564 −14.0695 21.5174 −3.12604 6.27806
1.14 −1.32200 −9.29623 −6.25232 6.03321 12.2896 36.0288 18.8415 59.4199 −7.97590
1.15 −1.21343 −0.584783 −6.52760 21.2304 0.709592 13.2251 17.6282 −26.6580 −25.7616
1.16 −0.568087 6.42425 −7.67728 4.18544 −3.64954 −32.4879 8.90606 14.2710 −2.37769
1.17 0.0313827 5.72009 −7.99902 7.55527 0.179512 −6.19881 −0.502093 5.71940 0.237105
1.18 0.305925 −0.688798 −7.90641 −14.6552 −0.210720 34.1750 −4.86616 −26.5256 −4.48337
1.19 0.495149 0.728931 −7.75483 −20.6600 0.360929 −8.57647 −7.80099 −26.4687 −10.2298
1.20 0.772290 8.82957 −7.40357 −17.1506 6.81899 3.36156 −11.8960 50.9614 −13.2452
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.o 34
11.b odd 2 1 1573.4.a.p 34
11.c even 5 2 143.4.h.a ✓ 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
143.4.h.a ✓ 68 11.c even 5 2
1573.4.a.o 34 1.a even 1 1 trivial
1573.4.a.p 34 11.b odd 2 1

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