Properties

Label 700.2.a.i
Level $700$
Weight $2$
Character orbit 700.a
Self dual yes
Analytic conductor $5.590$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{3} - q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - q^{7} + q^{9} + 3q^{11} + 4q^{13} + 2q^{19} - 2q^{21} + 3q^{23} - 4q^{27} + 9q^{29} + 8q^{31} + 6q^{33} - 5q^{37} + 8q^{39} - 6q^{41} - 11q^{43} - 6q^{47} + q^{49} - 6q^{53} + 4q^{57} - 10q^{61} - q^{63} - 5q^{67} + 6q^{69} + 15q^{71} + 10q^{73} - 3q^{77} - 7q^{79} - 11q^{81} - 12q^{83} + 18q^{87} - 12q^{89} - 4q^{91} + 16q^{93} - 8q^{97} + 3q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(7\) \(1\)

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 700.2.a.i yes 1
3.b odd 2 1 6300.2.a.e 1
4.b odd 2 1 2800.2.a.e 1
5.b even 2 1 700.2.a.c 1
5.c odd 4 2 700.2.e.b 2
7.b odd 2 1 4900.2.a.f 1
15.d odd 2 1 6300.2.a.s 1
15.e even 4 2 6300.2.k.d 2
20.d odd 2 1 2800.2.a.ba 1
20.e even 4 2 2800.2.g.e 2
35.c odd 2 1 4900.2.a.t 1
35.f even 4 2 4900.2.e.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
700.2.a.c 1 5.b even 2 1
700.2.a.i yes 1 1.a even 1 1 trivial
700.2.e.b 2 5.c odd 4 2
2800.2.a.e 1 4.b odd 2 1
2800.2.a.ba 1 20.d odd 2 1
2800.2.g.e 2 20.e even 4 2
4900.2.a.f 1 7.b odd 2 1
4900.2.a.t 1 35.c odd 2 1
4900.2.e.g 2 35.f even 4 2
6300.2.a.e 1 3.b odd 2 1
6300.2.a.s 1 15.d odd 2 1
6300.2.k.d 2 15.e even 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(700))\):

\( T_{3} - 2 \)
\( T_{11} - 3 \)
\( T_{13} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -2 + T \)
$5$ \( T \)
$7$ \( 1 + T \)
$11$ \( -3 + T \)
$13$ \( -4 + T \)
$17$ \( T \)
$19$ \( -2 + T \)
$23$ \( -3 + T \)
$29$ \( -9 + T \)
$31$ \( -8 + T \)
$37$ \( 5 + T \)
$41$ \( 6 + T \)
$43$ \( 11 + T \)
$47$ \( 6 + T \)
$53$ \( 6 + T \)
$59$ \( T \)
$61$ \( 10 + T \)
$67$ \( 5 + T \)
$71$ \( -15 + T \)
$73$ \( -10 + T \)
$79$ \( 7 + T \)
$83$ \( 12 + T \)
$89$ \( 12 + T \)
$97$ \( 8 + T \)
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