Properties

Label 2450.2.a.bc
Level $2450$
Weight $2$
Character orbit 2450.a
Self dual yes
Analytic conductor $19.563$
Analytic rank $1$
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: \(1\)
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

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

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.bc 1
5.b even 2 1 490.2.a.b 1
5.c odd 4 2 2450.2.c.l 2
7.b odd 2 1 2450.2.a.w 1
7.d odd 6 2 350.2.e.e 2
15.d odd 2 1 4410.2.a.bd 1
20.d odd 2 1 3920.2.a.bc 1
35.c odd 2 1 490.2.a.c 1
35.f even 4 2 2450.2.c.g 2
35.i odd 6 2 70.2.e.c 2
35.j even 6 2 490.2.e.h 2
35.k even 12 4 350.2.j.b 4
105.g even 2 1 4410.2.a.bm 1
105.p even 6 2 630.2.k.b 2
140.c even 2 1 3920.2.a.p 1
140.s even 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.i odd 6 2
350.2.e.e 2 7.d odd 6 2
350.2.j.b 4 35.k even 12 4
490.2.a.b 1 5.b even 2 1
490.2.a.c 1 35.c odd 2 1
490.2.e.h 2 35.j even 6 2
560.2.q.g 2 140.s even 6 2
630.2.k.b 2 105.p even 6 2
2450.2.a.w 1 7.b odd 2 1
2450.2.a.bc 1 1.a even 1 1 trivial
2450.2.c.g 2 35.f even 4 2
2450.2.c.l 2 5.c odd 4 2
3920.2.a.p 1 140.c even 2 1
3920.2.a.bc 1 20.d odd 2 1
4410.2.a.bd 1 15.d odd 2 1
4410.2.a.bm 1 105.g even 2 1

Hecke kernels

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

\( T_{3} - 1 \) Copy content Toggle raw display
\( T_{11} + 6 \) Copy content Toggle raw display
\( T_{13} + 4 \) Copy content Toggle raw display
\( T_{17} \) Copy content Toggle raw display
\( T_{19} + 2 \) Copy content Toggle raw display
\( T_{23} - 3 \) Copy content Toggle raw display
\( T_{37} - 4 \) Copy content Toggle raw display

Hecke characteristic polynomials

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