Properties

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

Related objects

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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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{7} + q^{8} - 3q^{9} - q^{11} - 2q^{13} + q^{14} + q^{16} + 4q^{17} - 3q^{18} - 6q^{19} - q^{22} - 4q^{23} - 2q^{26} + q^{28} - 2q^{29} - 2q^{31} + q^{32} + 4q^{34} - 3q^{36} - 10q^{37} - 6q^{38} + 4q^{41} + 8q^{43} - q^{44} - 4q^{46} - 2q^{47} + q^{49} - 2q^{52} - 6q^{53} + q^{56} - 2q^{58} - 12q^{59} - 14q^{61} - 2q^{62} - 3q^{63} + q^{64} + 12q^{67} + 4q^{68} - 8q^{71} - 3q^{72} - 4q^{73} - 10q^{74} - 6q^{76} - q^{77} + 9q^{81} + 4q^{82} + 6q^{83} + 8q^{86} - q^{88} - 6q^{89} - 2q^{91} - 4q^{92} - 2q^{94} + 14q^{97} + q^{98} + 3q^{99} + O(q^{100}) \)

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

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.u 1
5.b even 2 1 154.2.a.a 1
5.c odd 4 2 3850.2.c.j 2
15.d odd 2 1 1386.2.a.l 1
20.d odd 2 1 1232.2.a.e 1
35.c odd 2 1 1078.2.a.d 1
35.i odd 6 2 1078.2.e.i 2
35.j even 6 2 1078.2.e.j 2
40.e odd 2 1 4928.2.a.w 1
40.f even 2 1 4928.2.a.v 1
55.d odd 2 1 1694.2.a.g 1
105.g even 2 1 9702.2.a.ba 1
140.c even 2 1 8624.2.a.r 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.a 1 5.b even 2 1
1078.2.a.d 1 35.c odd 2 1
1078.2.e.i 2 35.i odd 6 2
1078.2.e.j 2 35.j even 6 2
1232.2.a.e 1 20.d odd 2 1
1386.2.a.l 1 15.d odd 2 1
1694.2.a.g 1 55.d odd 2 1
3850.2.a.u 1 1.a even 1 1 trivial
3850.2.c.j 2 5.c odd 4 2
4928.2.a.v 1 40.f even 2 1
4928.2.a.w 1 40.e odd 2 1
8624.2.a.r 1 140.c even 2 1
9702.2.a.ba 1 105.g even 2 1

Hecke kernels

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

\( T_{3} \)
\( T_{13} + 2 \)
\( T_{17} - 4 \)
\( T_{19} + 6 \)

Hecke characteristic polynomials

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