Properties

Label 2450.2.a.bh
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

Related objects

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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

\(f(q)\) \(=\) \( q + q^{2} + 3q^{3} + q^{4} + 3q^{6} + q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} + 3q^{3} + q^{4} + 3q^{6} + q^{8} + 6q^{9} + 3q^{12} + 2q^{13} + q^{16} + 2q^{17} + 6q^{18} + 2q^{19} - q^{23} + 3q^{24} + 2q^{26} + 9q^{27} - q^{29} - 10q^{31} + q^{32} + 2q^{34} + 6q^{36} - 8q^{37} + 2q^{38} + 6q^{39} + 3q^{41} + 5q^{43} - q^{46} - 8q^{47} + 3q^{48} + 6q^{51} + 2q^{52} - 6q^{53} + 9q^{54} + 6q^{57} - q^{58} - 2q^{59} + 9q^{61} - 10q^{62} + q^{64} - 7q^{67} + 2q^{68} - 3q^{69} + 6q^{71} + 6q^{72} + 10q^{73} - 8q^{74} + 2q^{76} + 6q^{78} - 10q^{79} + 9q^{81} + 3q^{82} + 9q^{83} + 5q^{86} - 3q^{87} + 7q^{89} - q^{92} - 30q^{93} - 8q^{94} + 3q^{96} + O(q^{100}) \)

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 3.00000 1.00000 0 3.00000 0 1.00000 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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.bh 1
5.b even 2 1 2450.2.a.c 1
5.c odd 4 2 490.2.c.b 2
7.b odd 2 1 2450.2.a.s 1
7.d odd 6 2 350.2.e.f 2
35.c odd 2 1 2450.2.a.r 1
35.f even 4 2 490.2.c.c 2
35.i odd 6 2 350.2.e.g 2
35.k even 12 4 70.2.i.a 4
35.l odd 12 4 490.2.i.b 4
105.w odd 12 4 630.2.u.b 4
140.x odd 12 4 560.2.bw.c 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.i.a 4 35.k even 12 4
350.2.e.f 2 7.d odd 6 2
350.2.e.g 2 35.i odd 6 2
490.2.c.b 2 5.c odd 4 2
490.2.c.c 2 35.f even 4 2
490.2.i.b 4 35.l odd 12 4
560.2.bw.c 4 140.x odd 12 4
630.2.u.b 4 105.w odd 12 4
2450.2.a.c 1 5.b even 2 1
2450.2.a.r 1 35.c odd 2 1
2450.2.a.s 1 7.b odd 2 1
2450.2.a.bh 1 1.a even 1 1 trivial

Atkin-Lehner signs

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

Hecke kernels

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

\( T_{3} - 3 \)
\( T_{11} \)
\( T_{13} - 2 \)
\( T_{17} - 2 \)
\( T_{19} - 2 \)
\( T_{23} + 1 \)
\( T_{37} + 8 \)

Hecke Characteristic Polynomials

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