Properties

Label 2450.2.a.z
Level $2450$
Weight $2$
Character orbit 2450.a
Self dual yes
Analytic conductor $19.563$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2450.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.5633484952\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 350)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{8} - 3q^{9} - 2q^{11} + q^{16} + 7q^{17} - 3q^{18} - 2q^{22} + 3q^{23} + 6q^{29} + 7q^{31} + q^{32} + 7q^{34} - 3q^{36} - 4q^{37} + 7q^{41} - 8q^{43} - 2q^{44} + 3q^{46} + 7q^{47} + 4q^{53} + 6q^{58} + 14q^{59} + 14q^{61} + 7q^{62} + q^{64} + 12q^{67} + 7q^{68} - q^{71} - 3q^{72} - 14q^{73} - 4q^{74} - 11q^{79} + 9q^{81} + 7q^{82} - 14q^{83} - 8q^{86} - 2q^{88} - 7q^{89} + 3q^{92} + 7q^{94} + 7q^{97} + 6q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

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

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 2450.2.a.z 1
5.b even 2 1 2450.2.a.h 1
5.c odd 4 2 2450.2.c.j 2
7.b odd 2 1 2450.2.a.y 1
7.d odd 6 2 350.2.e.d 2
35.c odd 2 1 2450.2.a.i 1
35.f even 4 2 2450.2.c.i 2
35.i odd 6 2 350.2.e.i yes 2
35.k even 12 4 350.2.j.c 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
350.2.e.d 2 7.d odd 6 2
350.2.e.i yes 2 35.i odd 6 2
350.2.j.c 4 35.k even 12 4
2450.2.a.h 1 5.b even 2 1
2450.2.a.i 1 35.c odd 2 1
2450.2.a.y 1 7.b odd 2 1
2450.2.a.z 1 1.a even 1 1 trivial
2450.2.c.i 2 35.f even 4 2
2450.2.c.j 2 5.c odd 4 2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2450))\):

\( T_{3} \)
\( T_{11} + 2 \)
\( T_{13} \)
\( T_{17} - 7 \)
\( T_{19} \)
\( T_{23} - 3 \)
\( T_{37} + 4 \)

Hecke characteristic polynomials

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