Properties

Label 1850.2.a.j
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: no (minimal twist has level 370)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 2q^{7} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} - 2q^{7} + q^{8} - 3q^{9} + 2q^{13} - 2q^{14} + q^{16} - 6q^{17} - 3q^{18} - 6q^{19} + 4q^{23} + 2q^{26} - 2q^{28} - 4q^{31} + q^{32} - 6q^{34} - 3q^{36} - q^{37} - 6q^{38} - 10q^{41} - 4q^{43} + 4q^{46} - 2q^{47} - 3q^{49} + 2q^{52} + 2q^{53} - 2q^{56} - 6q^{59} - 4q^{62} + 6q^{63} + q^{64} + 8q^{67} - 6q^{68} - 3q^{72} + 8q^{73} - q^{74} - 6q^{76} + 4q^{79} + 9q^{81} - 10q^{82} - 12q^{83} - 4q^{86} + 6q^{89} - 4q^{91} + 4q^{92} - 2q^{94} - 10q^{97} - 3q^{98} + O(q^{100}) \)

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 0 1.00000 0 0 −2.00000 1.00000 −3.00000 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.j 1
5.b even 2 1 1850.2.a.e 1
5.c odd 4 2 370.2.b.a 2
15.e even 4 2 3330.2.d.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
370.2.b.a 2 5.c odd 4 2
1850.2.a.e 1 5.b even 2 1
1850.2.a.j 1 1.a even 1 1 trivial
3330.2.d.f 2 15.e even 4 2

Hecke kernels

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( 2 + T \)
$11$ \( T \)
$13$ \( -2 + T \)
$17$ \( 6 + T \)
$19$ \( 6 + T \)
$23$ \( -4 + T \)
$29$ \( T \)
$31$ \( 4 + T \)
$37$ \( 1 + T \)
$41$ \( 10 + T \)
$43$ \( 4 + T \)
$47$ \( 2 + T \)
$53$ \( -2 + T \)
$59$ \( 6 + T \)
$61$ \( T \)
$67$ \( -8 + T \)
$71$ \( T \)
$73$ \( -8 + T \)
$79$ \( -4 + T \)
$83$ \( 12 + T \)
$89$ \( -6 + T \)
$97$ \( 10 + T \)
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