Properties

Label 1850.2.a.n
Level $1850$
Weight $2$
Character orbit 1850.a
Self dual yes
Analytic conductor $14.772$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1850.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.7723243739\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + 4q^{11} + 2q^{12} - 2q^{13} + q^{16} + 8q^{17} + q^{18} - 5q^{19} + 4q^{22} + q^{23} + 2q^{24} - 2q^{26} - 4q^{27} + 10q^{29} - 4q^{31} + q^{32} + 8q^{33} + 8q^{34} + q^{36} + q^{37} - 5q^{38} - 4q^{39} + 7q^{41} - 9q^{43} + 4q^{44} + q^{46} + 6q^{47} + 2q^{48} - 7q^{49} + 16q^{51} - 2q^{52} - 3q^{53} - 4q^{54} - 10q^{57} + 10q^{58} - 11q^{59} + 2q^{61} - 4q^{62} + q^{64} + 8q^{66} + 2q^{67} + 8q^{68} + 2q^{69} + 14q^{71} + q^{72} + 3q^{73} + q^{74} - 5q^{76} - 4q^{78} - 11q^{79} - 11q^{81} + 7q^{82} + 8q^{83} - 9q^{86} + 20q^{87} + 4q^{88} - 2q^{89} + q^{92} - 8q^{93} + 6q^{94} + 2q^{96} - 8q^{97} - 7q^{98} + 4q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(37\) \(-1\)

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 1850.2.a.n yes 1
5.b even 2 1 1850.2.a.b 1
5.c odd 4 2 1850.2.b.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1850.2.a.b 1 5.b even 2 1
1850.2.a.n yes 1 1.a even 1 1 trivial
1850.2.b.h 2 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\):

\( T_{3} - 2 \)
\( T_{7} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -2 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( -4 + T \)
$13$ \( 2 + T \)
$17$ \( -8 + T \)
$19$ \( 5 + T \)
$23$ \( -1 + T \)
$29$ \( -10 + T \)
$31$ \( 4 + T \)
$37$ \( -1 + T \)
$41$ \( -7 + T \)
$43$ \( 9 + T \)
$47$ \( -6 + T \)
$53$ \( 3 + T \)
$59$ \( 11 + T \)
$61$ \( -2 + T \)
$67$ \( -2 + T \)
$71$ \( -14 + T \)
$73$ \( -3 + T \)
$79$ \( 11 + T \)
$83$ \( -8 + T \)
$89$ \( 2 + T \)
$97$ \( 8 + T \)
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