Properties

Label 2450.2.a.w
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 70)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} - 2q^{9} - 6q^{11} - q^{12} + 4q^{13} + q^{16} - 2q^{18} + 2q^{19} - 6q^{22} + 3q^{23} - q^{24} + 4q^{26} + 5q^{27} - 3q^{29} + 8q^{31} + q^{32} + 6q^{33} - 2q^{36} + 4q^{37} + 2q^{38} - 4q^{39} + 9q^{41} + 7q^{43} - 6q^{44} + 3q^{46} - q^{48} + 4q^{52} + 6q^{53} + 5q^{54} - 2q^{57} - 3q^{58} - 6q^{59} + 5q^{61} + 8q^{62} + q^{64} + 6q^{66} - 5q^{67} - 3q^{69} - 6q^{71} - 2q^{72} + 16q^{73} + 4q^{74} + 2q^{76} - 4q^{78} + 2q^{79} + q^{81} + 9q^{82} - 3q^{83} + 7q^{86} + 3q^{87} - 6q^{88} - 15q^{89} + 3q^{92} - 8q^{93} - q^{96} - 14q^{97} + 12q^{99} + O(q^{100}) \)

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 0 −1.00000 0 1.00000 −2.00000 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.w 1
5.b even 2 1 490.2.a.c 1
5.c odd 4 2 2450.2.c.g 2
7.b odd 2 1 2450.2.a.bc 1
7.c even 3 2 350.2.e.e 2
15.d odd 2 1 4410.2.a.bm 1
20.d odd 2 1 3920.2.a.p 1
35.c odd 2 1 490.2.a.b 1
35.f even 4 2 2450.2.c.l 2
35.i odd 6 2 490.2.e.h 2
35.j even 6 2 70.2.e.c 2
35.l odd 12 4 350.2.j.b 4
105.g even 2 1 4410.2.a.bd 1
105.o odd 6 2 630.2.k.b 2
140.c even 2 1 3920.2.a.bc 1
140.p odd 6 2 560.2.q.g 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.e.c 2 35.j even 6 2
350.2.e.e 2 7.c even 3 2
350.2.j.b 4 35.l odd 12 4
490.2.a.b 1 35.c odd 2 1
490.2.a.c 1 5.b even 2 1
490.2.e.h 2 35.i odd 6 2
560.2.q.g 2 140.p odd 6 2
630.2.k.b 2 105.o odd 6 2
2450.2.a.w 1 1.a even 1 1 trivial
2450.2.a.bc 1 7.b odd 2 1
2450.2.c.g 2 5.c odd 4 2
2450.2.c.l 2 35.f even 4 2
3920.2.a.p 1 20.d odd 2 1
3920.2.a.bc 1 140.c even 2 1
4410.2.a.bd 1 105.g even 2 1
4410.2.a.bm 1 15.d odd 2 1

Hecke kernels

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

\( T_{3} + 1 \)
\( T_{11} + 6 \)
\( T_{13} - 4 \)
\( T_{17} \)
\( T_{19} - 2 \)
\( T_{23} - 3 \)
\( T_{37} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( 6 + T \)
$13$ \( -4 + T \)
$17$ \( T \)
$19$ \( -2 + T \)
$23$ \( -3 + T \)
$29$ \( 3 + T \)
$31$ \( -8 + T \)
$37$ \( -4 + T \)
$41$ \( -9 + T \)
$43$ \( -7 + T \)
$47$ \( T \)
$53$ \( -6 + T \)
$59$ \( 6 + T \)
$61$ \( -5 + T \)
$67$ \( 5 + T \)
$71$ \( 6 + T \)
$73$ \( -16 + T \)
$79$ \( -2 + T \)
$83$ \( 3 + T \)
$89$ \( 15 + T \)
$97$ \( 14 + T \)
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