Properties

Label 1849.2.a.d
Level 1849
Weight 2
Character orbit 1849.a
Self dual yes
Analytic conductor 14.764
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.7643393337\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{3} + 2q^{4} + 4q^{5} + 4q^{6} + q^{9} + O(q^{10}) \) \( q + 2q^{2} + 2q^{3} + 2q^{4} + 4q^{5} + 4q^{6} + q^{9} + 8q^{10} + 3q^{11} + 4q^{12} - 5q^{13} + 8q^{15} - 4q^{16} - 3q^{17} + 2q^{18} + 2q^{19} + 8q^{20} + 6q^{22} - q^{23} + 11q^{25} - 10q^{26} - 4q^{27} + 6q^{29} + 16q^{30} - q^{31} - 8q^{32} + 6q^{33} - 6q^{34} + 2q^{36} + 4q^{38} - 10q^{39} + 5q^{41} + 6q^{44} + 4q^{45} - 2q^{46} + 4q^{47} - 8q^{48} - 7q^{49} + 22q^{50} - 6q^{51} - 10q^{52} - 5q^{53} - 8q^{54} + 12q^{55} + 4q^{57} + 12q^{58} - 12q^{59} + 16q^{60} - 2q^{61} - 2q^{62} - 8q^{64} - 20q^{65} + 12q^{66} - 3q^{67} - 6q^{68} - 2q^{69} - 2q^{71} - 2q^{73} + 22q^{75} + 4q^{76} - 20q^{78} - 8q^{79} - 16q^{80} - 11q^{81} + 10q^{82} + 15q^{83} - 12q^{85} + 12q^{87} + 4q^{89} + 8q^{90} - 2q^{92} - 2q^{93} + 8q^{94} + 8q^{95} - 16q^{96} + 7q^{97} - 14q^{98} + 3q^{99} + O(q^{100}) \)

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
2.00000 2.00000 2.00000 4.00000 4.00000 0 0 1.00000 8.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 1849.2.a.d 1
43.b odd 2 1 43.2.a.a 1
129.d even 2 1 387.2.a.e 1
172.d even 2 1 688.2.a.b 1
215.d odd 2 1 1075.2.a.h 1
215.g even 4 2 1075.2.b.b 2
301.c even 2 1 2107.2.a.a 1
344.e even 2 1 2752.2.a.b 1
344.h odd 2 1 2752.2.a.f 1
473.d even 2 1 5203.2.a.a 1
516.h odd 2 1 6192.2.a.ba 1
559.d odd 2 1 7267.2.a.a 1
645.d even 2 1 9675.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.2.a.a 1 43.b odd 2 1
387.2.a.e 1 129.d even 2 1
688.2.a.b 1 172.d even 2 1
1075.2.a.h 1 215.d odd 2 1
1075.2.b.b 2 215.g even 4 2
1849.2.a.d 1 1.a even 1 1 trivial
2107.2.a.a 1 301.c even 2 1
2752.2.a.b 1 344.e even 2 1
2752.2.a.f 1 344.h odd 2 1
5203.2.a.a 1 473.d even 2 1
6192.2.a.ba 1 516.h odd 2 1
7267.2.a.a 1 559.d odd 2 1
9675.2.a.b 1 645.d even 2 1

Atkin-Lehner signs

\( p \) Sign
\(43\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T + 2 T^{2} \)
$3$ \( 1 - 2 T + 3 T^{2} \)
$5$ \( 1 - 4 T + 5 T^{2} \)
$7$ \( 1 + 7 T^{2} \)
$11$ \( 1 - 3 T + 11 T^{2} \)
$13$ \( 1 + 5 T + 13 T^{2} \)
$17$ \( 1 + 3 T + 17 T^{2} \)
$19$ \( 1 - 2 T + 19 T^{2} \)
$23$ \( 1 + T + 23 T^{2} \)
$29$ \( 1 - 6 T + 29 T^{2} \)
$31$ \( 1 + T + 31 T^{2} \)
$37$ \( 1 + 37 T^{2} \)
$41$ \( 1 - 5 T + 41 T^{2} \)
$43$ 1
$47$ \( 1 - 4 T + 47 T^{2} \)
$53$ \( 1 + 5 T + 53 T^{2} \)
$59$ \( 1 + 12 T + 59 T^{2} \)
$61$ \( 1 + 2 T + 61 T^{2} \)
$67$ \( 1 + 3 T + 67 T^{2} \)
$71$ \( 1 + 2 T + 71 T^{2} \)
$73$ \( 1 + 2 T + 73 T^{2} \)
$79$ \( 1 + 8 T + 79 T^{2} \)
$83$ \( 1 - 15 T + 83 T^{2} \)
$89$ \( 1 - 4 T + 89 T^{2} \)
$97$ \( 1 - 7 T + 97 T^{2} \)
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