Properties

Label 3850.2.a.f
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} - q^{11} - 2 q^{13} - q^{14} + q^{16} - 2 q^{17} + 3 q^{18} + q^{22} + 8 q^{23} + 2 q^{26} + q^{28} - 2 q^{29} - 8 q^{31} - q^{32} + 2 q^{34} - 3 q^{36} + 2 q^{37} + 10 q^{41} - 4 q^{43} - q^{44} - 8 q^{46} - 8 q^{47} + q^{49} - 2 q^{52} - 6 q^{53} - q^{56} + 2 q^{58} + 10 q^{61} + 8 q^{62} - 3 q^{63} + q^{64} + 12 q^{67} - 2 q^{68} + 16 q^{71} + 3 q^{72} + 14 q^{73} - 2 q^{74} - q^{77} + 9 q^{81} - 10 q^{82} + 4 q^{86} + q^{88} - 6 q^{89} - 2 q^{91} + 8 q^{92} + 8 q^{94} - 10 q^{97} - q^{98} + 3 q^{99}+O(q^{100}) \) 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 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.f 1
5.b even 2 1 154.2.a.c 1
5.c odd 4 2 3850.2.c.l 2
15.d odd 2 1 1386.2.a.b 1
20.d odd 2 1 1232.2.a.h 1
35.c odd 2 1 1078.2.a.j 1
35.i odd 6 2 1078.2.e.c 2
35.j even 6 2 1078.2.e.b 2
40.e odd 2 1 4928.2.a.o 1
40.f even 2 1 4928.2.a.n 1
55.d odd 2 1 1694.2.a.c 1
105.g even 2 1 9702.2.a.v 1
140.c even 2 1 8624.2.a.o 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.c 1 5.b even 2 1
1078.2.a.j 1 35.c odd 2 1
1078.2.e.b 2 35.j even 6 2
1078.2.e.c 2 35.i odd 6 2
1232.2.a.h 1 20.d odd 2 1
1386.2.a.b 1 15.d odd 2 1
1694.2.a.c 1 55.d odd 2 1
3850.2.a.f 1 1.a even 1 1 trivial
3850.2.c.l 2 5.c odd 4 2
4928.2.a.n 1 40.f even 2 1
4928.2.a.o 1 40.e odd 2 1
8624.2.a.o 1 140.c even 2 1
9702.2.a.v 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\):

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

Hecke characteristic polynomials

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