Properties

Label 1850.2.a.d
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} - 3 q^{11} + 4 q^{13} + q^{14} + q^{16} + 3 q^{17} + 3 q^{18} + 3 q^{22} + 8 q^{23} - 4 q^{26} - q^{28} - 3 q^{29} - 7 q^{31} - q^{32} - 3 q^{34} - 3 q^{36} + q^{37} + 11 q^{41} - 11 q^{43} - 3 q^{44} - 8 q^{46} - 4 q^{47} - 6 q^{49} + 4 q^{52} - 11 q^{53} + q^{56} + 3 q^{58} - 12 q^{59} - 15 q^{61} + 7 q^{62} + 3 q^{63} + q^{64} + 4 q^{67} + 3 q^{68} + 6 q^{71} + 3 q^{72} - 2 q^{73} - q^{74} + 3 q^{77} - 8 q^{79} + 9 q^{81} - 11 q^{82} - 12 q^{83} + 11 q^{86} + 3 q^{88} - 4 q^{91} + 8 q^{92} + 4 q^{94} + q^{97} + 6 q^{98} + 9 q^{99} + O(q^{100}) \)

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 0 1.00000 0 0 −1.00000 −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.d 1
5.b even 2 1 1850.2.a.l 1
5.c odd 4 2 370.2.b.b 2
15.e even 4 2 3330.2.d.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
370.2.b.b 2 5.c odd 4 2
1850.2.a.d 1 1.a even 1 1 trivial
1850.2.a.l 1 5.b even 2 1
3330.2.d.c 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1850))\):

\( T_{3} \)
\( T_{7} + 1 \)

Hecke characteristic polynomials

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