Properties

Label 3850.2.a.o
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 154)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} + q^{7} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} + q^{7} + q^{8} + q^{9} + q^{11} - 2 q^{12} + 4 q^{13} + q^{14} + q^{16} + q^{18} + 4 q^{19} - 2 q^{21} + q^{22} - 4 q^{23} - 2 q^{24} + 4 q^{26} + 4 q^{27} + q^{28} + 2 q^{29} - 10 q^{31} + q^{32} - 2 q^{33} + q^{36} + 6 q^{37} + 4 q^{38} - 8 q^{39} - 2 q^{42} + 4 q^{43} + q^{44} - 4 q^{46} - 10 q^{47} - 2 q^{48} + q^{49} + 4 q^{52} + 14 q^{53} + 4 q^{54} + q^{56} - 8 q^{57} + 2 q^{58} + 10 q^{59} - 8 q^{61} - 10 q^{62} + q^{63} + q^{64} - 2 q^{66} - 8 q^{67} + 8 q^{69} - 4 q^{71} + q^{72} - 4 q^{73} + 6 q^{74} + 4 q^{76} + q^{77} - 8 q^{78} + 16 q^{79} - 11 q^{81} - 4 q^{83} - 2 q^{84} + 4 q^{86} - 4 q^{87} + q^{88} + 10 q^{89} + 4 q^{91} - 4 q^{92} + 20 q^{93} - 10 q^{94} - 2 q^{96} - 6 q^{97} + q^{98} + q^{99}+O(q^{100}) \) Copy content Toggle raw display

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.o 1
5.b even 2 1 154.2.a.b 1
5.c odd 4 2 3850.2.c.d 2
15.d odd 2 1 1386.2.a.f 1
20.d odd 2 1 1232.2.a.c 1
35.c odd 2 1 1078.2.a.b 1
35.i odd 6 2 1078.2.e.l 2
35.j even 6 2 1078.2.e.h 2
40.e odd 2 1 4928.2.a.bf 1
40.f even 2 1 4928.2.a.d 1
55.d odd 2 1 1694.2.a.i 1
105.g even 2 1 9702.2.a.bz 1
140.c even 2 1 8624.2.a.z 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.b 1 5.b even 2 1
1078.2.a.b 1 35.c odd 2 1
1078.2.e.h 2 35.j even 6 2
1078.2.e.l 2 35.i odd 6 2
1232.2.a.c 1 20.d odd 2 1
1386.2.a.f 1 15.d odd 2 1
1694.2.a.i 1 55.d odd 2 1
3850.2.a.o 1 1.a even 1 1 trivial
3850.2.c.d 2 5.c odd 4 2
4928.2.a.d 1 40.f even 2 1
4928.2.a.bf 1 40.e odd 2 1
8624.2.a.z 1 140.c even 2 1
9702.2.a.bz 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\):

\( T_{3} + 2 \) Copy content Toggle raw display
\( T_{13} - 4 \) Copy content Toggle raw display
\( T_{17} \) Copy content Toggle raw display
\( T_{19} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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