Properties

Label 2450.4.a.i
Level $2450$
Weight $4$
Character orbit 2450.a
Self dual yes
Analytic conductor $144.555$
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: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2450.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(144.554679514\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} - 2q^{3} + 4q^{4} + 4q^{6} - 8q^{8} - 23q^{9} + O(q^{10}) \) \( q - 2q^{2} - 2q^{3} + 4q^{4} + 4q^{6} - 8q^{8} - 23q^{9} + 48q^{11} - 8q^{12} + 56q^{13} + 16q^{16} - 114q^{17} + 46q^{18} - 2q^{19} - 96q^{22} + 120q^{23} + 16q^{24} - 112q^{26} + 100q^{27} - 54q^{29} - 236q^{31} - 32q^{32} - 96q^{33} + 228q^{34} - 92q^{36} - 146q^{37} + 4q^{38} - 112q^{39} - 126q^{41} + 376q^{43} + 192q^{44} - 240q^{46} - 12q^{47} - 32q^{48} + 228q^{51} + 224q^{52} - 174q^{53} - 200q^{54} + 4q^{57} + 108q^{58} - 138q^{59} - 380q^{61} + 472q^{62} + 64q^{64} + 192q^{66} + 484q^{67} - 456q^{68} - 240q^{69} + 576q^{71} + 184q^{72} - 1150q^{73} + 292q^{74} - 8q^{76} + 224q^{78} + 776q^{79} + 421q^{81} + 252q^{82} + 378q^{83} - 752q^{86} + 108q^{87} - 384q^{88} + 390q^{89} + 480q^{92} + 472q^{93} + 24q^{94} + 64q^{96} - 1330q^{97} - 1104q^{99} + O(q^{100}) \)

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
−2.00000 −2.00000 4.00000 0 4.00000 0 −8.00000 −23.0000 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 2450.4.a.i 1
5.b even 2 1 98.4.a.e 1
7.b odd 2 1 350.4.a.f 1
15.d odd 2 1 882.4.a.b 1
20.d odd 2 1 784.4.a.h 1
35.c odd 2 1 14.4.a.b 1
35.f even 4 2 350.4.c.g 2
35.i odd 6 2 98.4.c.c 2
35.j even 6 2 98.4.c.b 2
105.g even 2 1 126.4.a.d 1
105.o odd 6 2 882.4.g.v 2
105.p even 6 2 882.4.g.p 2
140.c even 2 1 112.4.a.e 1
280.c odd 2 1 448.4.a.k 1
280.n even 2 1 448.4.a.g 1
385.h even 2 1 1694.4.a.b 1
420.o odd 2 1 1008.4.a.r 1
455.h odd 2 1 2366.4.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.a.b 1 35.c odd 2 1
98.4.a.e 1 5.b even 2 1
98.4.c.b 2 35.j even 6 2
98.4.c.c 2 35.i odd 6 2
112.4.a.e 1 140.c even 2 1
126.4.a.d 1 105.g even 2 1
350.4.a.f 1 7.b odd 2 1
350.4.c.g 2 35.f even 4 2
448.4.a.g 1 280.n even 2 1
448.4.a.k 1 280.c odd 2 1
784.4.a.h 1 20.d odd 2 1
882.4.a.b 1 15.d odd 2 1
882.4.g.p 2 105.p even 6 2
882.4.g.v 2 105.o odd 6 2
1008.4.a.r 1 420.o odd 2 1
1694.4.a.b 1 385.h even 2 1
2366.4.a.c 1 455.h odd 2 1
2450.4.a.i 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2450))\):

\( T_{3} + 2 \)
\( T_{11} - 48 \)
\( T_{19} + 2 \)
\( T_{23} - 120 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( 2 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( -48 + T \)
$13$ \( -56 + T \)
$17$ \( 114 + T \)
$19$ \( 2 + T \)
$23$ \( -120 + T \)
$29$ \( 54 + T \)
$31$ \( 236 + T \)
$37$ \( 146 + T \)
$41$ \( 126 + T \)
$43$ \( -376 + T \)
$47$ \( 12 + T \)
$53$ \( 174 + T \)
$59$ \( 138 + T \)
$61$ \( 380 + T \)
$67$ \( -484 + T \)
$71$ \( -576 + T \)
$73$ \( 1150 + T \)
$79$ \( -776 + T \)
$83$ \( -378 + T \)
$89$ \( -390 + T \)
$97$ \( 1330 + T \)
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