Properties

Label 1850.2.a.h
Level $1850$
Weight $2$
Character orbit 1850.a
Self dual yes
Analytic conductor $14.772$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} - 3 q^{3} + q^{4} - 3 q^{6} + q^{8} + 6 q^{9} + O(q^{10}) \) \( q + q^{2} - 3 q^{3} + q^{4} - 3 q^{6} + q^{8} + 6 q^{9} - q^{11} - 3 q^{12} - 2 q^{13} + q^{16} - 7 q^{17} + 6 q^{18} + 5 q^{19} - q^{22} + 6 q^{23} - 3 q^{24} - 2 q^{26} - 9 q^{27} - 4 q^{31} + q^{32} + 3 q^{33} - 7 q^{34} + 6 q^{36} + q^{37} + 5 q^{38} + 6 q^{39} - 3 q^{41} - 4 q^{43} - q^{44} + 6 q^{46} - 4 q^{47} - 3 q^{48} - 7 q^{49} + 21 q^{51} - 2 q^{52} + 2 q^{53} - 9 q^{54} - 15 q^{57} + 4 q^{59} - 8 q^{61} - 4 q^{62} + q^{64} + 3 q^{66} - 13 q^{67} - 7 q^{68} - 18 q^{69} - 6 q^{71} + 6 q^{72} - 7 q^{73} + q^{74} + 5 q^{76} + 6 q^{78} + 14 q^{79} + 9 q^{81} - 3 q^{82} + 3 q^{83} - 4 q^{86} - q^{88} - 7 q^{89} + 6 q^{92} + 12 q^{93} - 4 q^{94} - 3 q^{96} - 18 q^{97} - 7 q^{98} - 6 q^{99} + O(q^{100}) \)

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 −3.00000 1.00000 0 −3.00000 0 1.00000 6.00000 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.h yes 1
5.b even 2 1 1850.2.a.g 1
5.c odd 4 2 1850.2.b.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1850.2.a.g 1 5.b even 2 1
1850.2.a.h yes 1 1.a even 1 1 trivial
1850.2.b.a 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\):

\( T_{3} + 3 \)
\( T_{7} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 3 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( 1 + T \)
$13$ \( 2 + T \)
$17$ \( 7 + T \)
$19$ \( -5 + T \)
$23$ \( -6 + T \)
$29$ \( T \)
$31$ \( 4 + T \)
$37$ \( -1 + T \)
$41$ \( 3 + T \)
$43$ \( 4 + T \)
$47$ \( 4 + T \)
$53$ \( -2 + T \)
$59$ \( -4 + T \)
$61$ \( 8 + T \)
$67$ \( 13 + T \)
$71$ \( 6 + T \)
$73$ \( 7 + T \)
$79$ \( -14 + T \)
$83$ \( -3 + T \)
$89$ \( 7 + T \)
$97$ \( 18 + T \)
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