Properties

Label 1573.4.a.a
Level $1573$
Weight $4$
Character orbit 1573.a
Self dual yes
Analytic conductor $92.810$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1573 = 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1573.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(92.8100044390\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 5 q^{2} - 7 q^{3} + 17 q^{4} - 7 q^{5} - 35 q^{6} + 13 q^{7} + 45 q^{8} + 22 q^{9} + O(q^{10}) \) \( q + 5 q^{2} - 7 q^{3} + 17 q^{4} - 7 q^{5} - 35 q^{6} + 13 q^{7} + 45 q^{8} + 22 q^{9} - 35 q^{10} - 119 q^{12} - 13 q^{13} + 65 q^{14} + 49 q^{15} + 89 q^{16} - 77 q^{17} + 110 q^{18} + 126 q^{19} - 119 q^{20} - 91 q^{21} - 96 q^{23} - 315 q^{24} - 76 q^{25} - 65 q^{26} + 35 q^{27} + 221 q^{28} + 82 q^{29} + 245 q^{30} + 196 q^{31} + 85 q^{32} - 385 q^{34} - 91 q^{35} + 374 q^{36} - 131 q^{37} + 630 q^{38} + 91 q^{39} - 315 q^{40} - 336 q^{41} - 455 q^{42} + 201 q^{43} - 154 q^{45} - 480 q^{46} - 105 q^{47} - 623 q^{48} - 174 q^{49} - 380 q^{50} + 539 q^{51} - 221 q^{52} - 432 q^{53} + 175 q^{54} + 585 q^{56} - 882 q^{57} + 410 q^{58} - 294 q^{59} + 833 q^{60} + 56 q^{61} + 980 q^{62} + 286 q^{63} - 287 q^{64} + 91 q^{65} + 478 q^{67} - 1309 q^{68} + 672 q^{69} - 455 q^{70} + 9 q^{71} + 990 q^{72} - 98 q^{73} - 655 q^{74} + 532 q^{75} + 2142 q^{76} + 455 q^{78} - 1304 q^{79} - 623 q^{80} - 839 q^{81} - 1680 q^{82} + 308 q^{83} - 1547 q^{84} + 539 q^{85} + 1005 q^{86} - 574 q^{87} - 1190 q^{89} - 770 q^{90} - 169 q^{91} - 1632 q^{92} - 1372 q^{93} - 525 q^{94} - 882 q^{95} - 595 q^{96} + 70 q^{97} - 870 q^{98} + O(q^{100}) \)

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.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
5.00000 −7.00000 17.0000 −7.00000 −35.0000 13.0000 45.0000 22.0000 −35.0000
\(n\): e.g. 2-40 or 990-1000
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.a 1
11.b odd 2 1 13.4.a.a 1
33.d even 2 1 117.4.a.b 1
44.c even 2 1 208.4.a.g 1
55.d odd 2 1 325.4.a.d 1
55.e even 4 2 325.4.b.b 2
77.b even 2 1 637.4.a.a 1
88.b odd 2 1 832.4.a.r 1
88.g even 2 1 832.4.a.a 1
132.d odd 2 1 1872.4.a.k 1
143.d odd 2 1 169.4.a.e 1
143.g even 4 2 169.4.b.a 2
143.i odd 6 2 169.4.c.a 2
143.k odd 6 2 169.4.c.e 2
143.o even 12 4 169.4.e.e 4
429.e even 2 1 1521.4.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
13.4.a.a 1 11.b odd 2 1
117.4.a.b 1 33.d even 2 1
169.4.a.e 1 143.d odd 2 1
169.4.b.a 2 143.g even 4 2
169.4.c.a 2 143.i odd 6 2
169.4.c.e 2 143.k odd 6 2
169.4.e.e 4 143.o even 12 4
208.4.a.g 1 44.c even 2 1
325.4.a.d 1 55.d odd 2 1
325.4.b.b 2 55.e even 4 2
637.4.a.a 1 77.b even 2 1
832.4.a.a 1 88.g even 2 1
832.4.a.r 1 88.b odd 2 1
1521.4.a.a 1 429.e even 2 1
1573.4.a.a 1 1.a even 1 1 trivial
1872.4.a.k 1 132.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 5 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1573))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -5 + T \)
$3$ \( 7 + T \)
$5$ \( 7 + T \)
$7$ \( -13 + T \)
$11$ \( T \)
$13$ \( 13 + T \)
$17$ \( 77 + T \)
$19$ \( -126 + T \)
$23$ \( 96 + T \)
$29$ \( -82 + T \)
$31$ \( -196 + T \)
$37$ \( 131 + T \)
$41$ \( 336 + T \)
$43$ \( -201 + T \)
$47$ \( 105 + T \)
$53$ \( 432 + T \)
$59$ \( 294 + T \)
$61$ \( -56 + T \)
$67$ \( -478 + T \)
$71$ \( -9 + T \)
$73$ \( 98 + T \)
$79$ \( 1304 + T \)
$83$ \( -308 + T \)
$89$ \( 1190 + T \)
$97$ \( -70 + T \)
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