Properties

Label 4235.2.a.g
Level $4235$
Weight $2$
Character orbit 4235.a
Self dual yes
Analytic conductor $33.817$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4235.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(33.8166452560\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 385)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + q^{5} + q^{7} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} + q^{5} + q^{7} - 3q^{8} - 3q^{9} + q^{10} + 6q^{13} + q^{14} - q^{16} - 6q^{17} - 3q^{18} + 4q^{19} - q^{20} - 8q^{23} + q^{25} + 6q^{26} - q^{28} + 10q^{29} - 4q^{31} + 5q^{32} - 6q^{34} + q^{35} + 3q^{36} + 6q^{37} + 4q^{38} - 3q^{40} + 10q^{41} - 4q^{43} - 3q^{45} - 8q^{46} - 4q^{47} + q^{49} + q^{50} - 6q^{52} + 6q^{53} - 3q^{56} + 10q^{58} + 6q^{61} - 4q^{62} - 3q^{63} + 7q^{64} + 6q^{65} + 4q^{67} + 6q^{68} + q^{70} + 9q^{72} - 6q^{73} + 6q^{74} - 4q^{76} + 8q^{79} - q^{80} + 9q^{81} + 10q^{82} - 12q^{83} - 6q^{85} - 4q^{86} + 10q^{89} - 3q^{90} + 6q^{91} + 8q^{92} - 4q^{94} + 4q^{95} + 10q^{97} + q^{98} + O(q^{100}) \)

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 1.00000 0 1.00000 −3.00000 −3.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 4235.2.a.g 1
11.b odd 2 1 385.2.a.b 1
33.d even 2 1 3465.2.a.k 1
44.c even 2 1 6160.2.a.g 1
55.d odd 2 1 1925.2.a.i 1
55.e even 4 2 1925.2.b.b 2
77.b even 2 1 2695.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
385.2.a.b 1 11.b odd 2 1
1925.2.a.i 1 55.d odd 2 1
1925.2.b.b 2 55.e even 4 2
2695.2.a.a 1 77.b even 2 1
3465.2.a.k 1 33.d even 2 1
4235.2.a.g 1 1.a even 1 1 trivial
6160.2.a.g 1 44.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4235))\):

\( T_{2} - 1 \)
\( T_{3} \)
\( T_{13} - 6 \)

Hecke characteristic polynomials

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