Properties

Label 3234.2.a.v
Level $3234$
Weight $2$
Character orbit 3234.a
Self dual yes
Analytic conductor $25.824$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.8236200137\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} + q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} + q^{8} + q^{9} + 4 q^{10} - q^{11} + q^{12} + 6 q^{13} + 4 q^{15} + q^{16} + 4 q^{17} + q^{18} + 2 q^{19} + 4 q^{20} - q^{22} - 8 q^{23} + q^{24} + 11 q^{25} + 6 q^{26} + q^{27} - 6 q^{29} + 4 q^{30} - 6 q^{31} + q^{32} - q^{33} + 4 q^{34} + q^{36} - 6 q^{37} + 2 q^{38} + 6 q^{39} + 4 q^{40} - 12 q^{41} + 4 q^{43} - q^{44} + 4 q^{45} - 8 q^{46} - 6 q^{47} + q^{48} + 11 q^{50} + 4 q^{51} + 6 q^{52} + 2 q^{53} + q^{54} - 4 q^{55} + 2 q^{57} - 6 q^{58} + 4 q^{60} - 10 q^{61} - 6 q^{62} + q^{64} + 24 q^{65} - q^{66} + 4 q^{67} + 4 q^{68} - 8 q^{69} - 12 q^{71} + q^{72} - 6 q^{74} + 11 q^{75} + 2 q^{76} + 6 q^{78} - 16 q^{79} + 4 q^{80} + q^{81} - 12 q^{82} + 14 q^{83} + 16 q^{85} + 4 q^{86} - 6 q^{87} - q^{88} + 14 q^{89} + 4 q^{90} - 8 q^{92} - 6 q^{93} - 6 q^{94} + 8 q^{95} + q^{96} + 14 q^{97} - q^{99}+O(q^{100}) \) 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 1.00000 1.00000 4.00000 1.00000 0 1.00000 1.00000 4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(-1\)
\(11\) \(1\)

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 3234.2.a.v 1
3.b odd 2 1 9702.2.a.b 1
7.b odd 2 1 462.2.a.e 1
21.c even 2 1 1386.2.a.e 1
28.d even 2 1 3696.2.a.p 1
77.b even 2 1 5082.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
462.2.a.e 1 7.b odd 2 1
1386.2.a.e 1 21.c even 2 1
3234.2.a.v 1 1.a even 1 1 trivial
3696.2.a.p 1 28.d even 2 1
5082.2.a.a 1 77.b even 2 1
9702.2.a.b 1 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\):

\( T_{5} - 4 \) Copy content Toggle raw display
\( T_{13} - 6 \) Copy content Toggle raw display
\( T_{17} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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