Properties

Label 3850.2.a.bb
Level $3850$
Weight $2$
Character orbit 3850.a
Self dual yes
Analytic conductor $30.742$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3850.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(30.7424047782\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 770)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{7} + q^{8} + q^{9} + q^{11} + 2q^{12} + q^{14} + q^{16} + q^{18} + 2q^{21} + q^{22} + 4q^{23} + 2q^{24} - 4q^{27} + q^{28} + 2q^{29} - 2q^{31} + q^{32} + 2q^{33} + q^{36} + 6q^{37} + 8q^{41} + 2q^{42} + 12q^{43} + q^{44} + 4q^{46} + 6q^{47} + 2q^{48} + q^{49} + 6q^{53} - 4q^{54} + q^{56} + 2q^{58} - 10q^{59} - 4q^{61} - 2q^{62} + q^{63} + q^{64} + 2q^{66} + 8q^{67} + 8q^{69} - 4q^{71} + q^{72} + 4q^{73} + 6q^{74} + q^{77} - 16q^{79} - 11q^{81} + 8q^{82} + 2q^{84} + 12q^{86} + 4q^{87} + q^{88} - 6q^{89} + 4q^{92} - 4q^{93} + 6q^{94} + 2q^{96} - 14q^{97} + q^{98} + q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)
\(11\) \(-1\)

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 3850.2.a.bb 1
5.b even 2 1 770.2.a.b 1
5.c odd 4 2 3850.2.c.p 2
15.d odd 2 1 6930.2.a.s 1
20.d odd 2 1 6160.2.a.p 1
35.c odd 2 1 5390.2.a.q 1
55.d odd 2 1 8470.2.a.v 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
770.2.a.b 1 5.b even 2 1
3850.2.a.bb 1 1.a even 1 1 trivial
3850.2.c.p 2 5.c odd 4 2
5390.2.a.q 1 35.c odd 2 1
6160.2.a.p 1 20.d odd 2 1
6930.2.a.s 1 15.d odd 2 1
8470.2.a.v 1 55.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\):

\( T_{3} - 2 \)
\( T_{13} \)
\( T_{17} \)
\( T_{19} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -2 + T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( -1 + T \)
$13$ \( T \)
$17$ \( T \)
$19$ \( T \)
$23$ \( -4 + T \)
$29$ \( -2 + T \)
$31$ \( 2 + T \)
$37$ \( -6 + T \)
$41$ \( -8 + T \)
$43$ \( -12 + T \)
$47$ \( -6 + T \)
$53$ \( -6 + T \)
$59$ \( 10 + T \)
$61$ \( 4 + T \)
$67$ \( -8 + T \)
$71$ \( 4 + T \)
$73$ \( -4 + T \)
$79$ \( 16 + T \)
$83$ \( T \)
$89$ \( 6 + T \)
$97$ \( 14 + T \)
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