Properties

Label 1849.2.a.c
Level $1849$
Weight $2$
Character orbit 1849.a
Self dual yes
Analytic conductor $14.764$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} + 3q^{7} - 3q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} + 3q^{7} - 3q^{8} - 2q^{9} - q^{10} - q^{12} - 5q^{13} + 3q^{14} - q^{15} - q^{16} + 3q^{17} - 2q^{18} + q^{19} + q^{20} + 3q^{21} - 7q^{23} - 3q^{24} - 4q^{25} - 5q^{26} - 5q^{27} - 3q^{28} + 3q^{29} - q^{30} + 5q^{31} + 5q^{32} + 3q^{34} - 3q^{35} + 2q^{36} - 9q^{37} + q^{38} - 5q^{39} + 3q^{40} - 10q^{41} + 3q^{42} + 2q^{45} - 7q^{46} - 8q^{47} - q^{48} + 2q^{49} - 4q^{50} + 3q^{51} + 5q^{52} - 5q^{53} - 5q^{54} - 9q^{56} + q^{57} + 3q^{58} + 12q^{59} + q^{60} - 13q^{61} + 5q^{62} - 6q^{63} + 7q^{64} + 5q^{65} - 3q^{67} - 3q^{68} - 7q^{69} - 3q^{70} - q^{71} + 6q^{72} + 11q^{73} - 9q^{74} - 4q^{75} - q^{76} - 5q^{78} - 5q^{79} + q^{80} + q^{81} - 10q^{82} + 9q^{83} - 3q^{84} - 3q^{85} + 3q^{87} - q^{89} + 2q^{90} - 15q^{91} + 7q^{92} + 5q^{93} - 8q^{94} - q^{95} + 5q^{96} - 2q^{97} + 2q^{98} + O(q^{100}) \)

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
1.00000 1.00000 −1.00000 −1.00000 1.00000 3.00000 −3.00000 −2.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 1849.2.a.c 1
43.b odd 2 1 1849.2.a.a 1
43.c even 3 2 43.2.c.a 2
129.f odd 6 2 387.2.h.a 2
172.g odd 6 2 688.2.i.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
43.2.c.a 2 43.c even 3 2
387.2.h.a 2 129.f odd 6 2
688.2.i.d 2 172.g odd 6 2
1849.2.a.a 1 43.b odd 2 1
1849.2.a.c 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1849))\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + 2 T^{2} \)
$3$ \( 1 - T + 3 T^{2} \)
$5$ \( 1 + T + 5 T^{2} \)
$7$ \( 1 - 3 T + 7 T^{2} \)
$11$ \( 1 + 11 T^{2} \)
$13$ \( 1 + 5 T + 13 T^{2} \)
$17$ \( 1 - 3 T + 17 T^{2} \)
$19$ \( 1 - T + 19 T^{2} \)
$23$ \( 1 + 7 T + 23 T^{2} \)
$29$ \( 1 - 3 T + 29 T^{2} \)
$31$ \( 1 - 5 T + 31 T^{2} \)
$37$ \( 1 + 9 T + 37 T^{2} \)
$41$ \( 1 + 10 T + 41 T^{2} \)
$43$ 1
$47$ \( 1 + 8 T + 47 T^{2} \)
$53$ \( 1 + 5 T + 53 T^{2} \)
$59$ \( 1 - 12 T + 59 T^{2} \)
$61$ \( 1 + 13 T + 61 T^{2} \)
$67$ \( 1 + 3 T + 67 T^{2} \)
$71$ \( 1 + T + 71 T^{2} \)
$73$ \( 1 - 11 T + 73 T^{2} \)
$79$ \( 1 + 5 T + 79 T^{2} \)
$83$ \( 1 - 9 T + 83 T^{2} \)
$89$ \( 1 + T + 89 T^{2} \)
$97$ \( 1 + 2 T + 97 T^{2} \)
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