Properties

Label 1734.2.a.j
Level $1734$
Weight $2$
Character orbit 1734.a
Self dual yes
Analytic conductor $13.846$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1734.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.8460597105\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 102)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 2q^{13} - 2q^{15} + q^{16} + q^{18} + 4q^{19} + 2q^{20} + 4q^{22} - q^{24} - q^{25} - 2q^{26} - q^{27} + 10q^{29} - 2q^{30} - 8q^{31} + q^{32} - 4q^{33} + q^{36} + 2q^{37} + 4q^{38} + 2q^{39} + 2q^{40} - 10q^{41} + 12q^{43} + 4q^{44} + 2q^{45} - q^{48} - 7q^{49} - q^{50} - 2q^{52} + 6q^{53} - q^{54} + 8q^{55} - 4q^{57} + 10q^{58} + 12q^{59} - 2q^{60} + 10q^{61} - 8q^{62} + q^{64} - 4q^{65} - 4q^{66} - 12q^{67} + q^{72} - 10q^{73} + 2q^{74} + q^{75} + 4q^{76} + 2q^{78} + 8q^{79} + 2q^{80} + q^{81} - 10q^{82} + 4q^{83} + 12q^{86} - 10q^{87} + 4q^{88} - 6q^{89} + 2q^{90} + 8q^{93} + 8q^{95} - q^{96} + 14q^{97} - 7q^{98} + 4q^{99} + O(q^{100}) \)

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 −1.00000 1.00000 2.00000 −1.00000 0 1.00000 1.00000 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(17\) \(1\)

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 1734.2.a.j 1
3.b odd 2 1 5202.2.a.c 1
17.b even 2 1 102.2.a.c 1
17.c even 4 2 1734.2.b.b 2
17.d even 8 4 1734.2.f.e 4
51.c odd 2 1 306.2.a.b 1
68.d odd 2 1 816.2.a.b 1
85.c even 2 1 2550.2.a.c 1
85.g odd 4 2 2550.2.d.m 2
119.d odd 2 1 4998.2.a.be 1
136.e odd 2 1 3264.2.a.bc 1
136.h even 2 1 3264.2.a.m 1
204.h even 2 1 2448.2.a.p 1
255.h odd 2 1 7650.2.a.ca 1
408.b odd 2 1 9792.2.a.k 1
408.h even 2 1 9792.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
102.2.a.c 1 17.b even 2 1
306.2.a.b 1 51.c odd 2 1
816.2.a.b 1 68.d odd 2 1
1734.2.a.j 1 1.a even 1 1 trivial
1734.2.b.b 2 17.c even 4 2
1734.2.f.e 4 17.d even 8 4
2448.2.a.p 1 204.h even 2 1
2550.2.a.c 1 85.c even 2 1
2550.2.d.m 2 85.g odd 4 2
3264.2.a.m 1 136.h even 2 1
3264.2.a.bc 1 136.e odd 2 1
4998.2.a.be 1 119.d odd 2 1
5202.2.a.c 1 3.b odd 2 1
7650.2.a.ca 1 255.h odd 2 1
9792.2.a.k 1 408.b odd 2 1
9792.2.a.l 1 408.h even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\):

\( T_{5} - 2 \)
\( T_{7} \)

Hecke characteristic polynomials

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