Properties

Label 2450.4.a.bh
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

Related objects

Downloads

Learn more about

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

\(f(q)\) \(=\) \( q + 2q^{2} + q^{3} + 4q^{4} + 2q^{6} + 8q^{8} - 26q^{9} + O(q^{10}) \) \( q + 2q^{2} + q^{3} + 4q^{4} + 2q^{6} + 8q^{8} - 26q^{9} + 35q^{11} + 4q^{12} - 66q^{13} + 16q^{16} - 59q^{17} - 52q^{18} + 137q^{19} + 70q^{22} + 7q^{23} + 8q^{24} - 132q^{26} - 53q^{27} + 106q^{29} + 75q^{31} + 32q^{32} + 35q^{33} - 118q^{34} - 104q^{36} - 11q^{37} + 274q^{38} - 66q^{39} - 498q^{41} - 260q^{43} + 140q^{44} + 14q^{46} + 171q^{47} + 16q^{48} - 59q^{51} - 264q^{52} + 417q^{53} - 106q^{54} + 137q^{57} + 212q^{58} - 17q^{59} + 51q^{61} + 150q^{62} + 64q^{64} + 70q^{66} - 439q^{67} - 236q^{68} + 7q^{69} - 784q^{71} - 208q^{72} - 295q^{73} - 22q^{74} + 548q^{76} - 132q^{78} - 495q^{79} + 649q^{81} - 996q^{82} - 932q^{83} - 520q^{86} + 106q^{87} + 280q^{88} - 873q^{89} + 28q^{92} + 75q^{93} + 342q^{94} + 32q^{96} + 290q^{97} - 910q^{99} + O(q^{100}) \)

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 1.00000 4.00000 0 2.00000 0 8.00000 −26.0000 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 2450.4.a.bh 1
5.b even 2 1 98.4.a.b 1
7.b odd 2 1 2450.4.a.bf 1
7.c even 3 2 350.4.e.b 2
15.d odd 2 1 882.4.a.k 1
20.d odd 2 1 784.4.a.l 1
35.c odd 2 1 98.4.a.c 1
35.i odd 6 2 98.4.c.e 2
35.j even 6 2 14.4.c.b 2
35.l odd 12 4 350.4.j.d 4
105.g even 2 1 882.4.a.p 1
105.o odd 6 2 126.4.g.c 2
105.p even 6 2 882.4.g.d 2
140.c even 2 1 784.4.a.j 1
140.p odd 6 2 112.4.i.b 2
280.bf even 6 2 448.4.i.c 2
280.bi odd 6 2 448.4.i.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.c.b 2 35.j even 6 2
98.4.a.b 1 5.b even 2 1
98.4.a.c 1 35.c odd 2 1
98.4.c.e 2 35.i odd 6 2
112.4.i.b 2 140.p odd 6 2
126.4.g.c 2 105.o odd 6 2
350.4.e.b 2 7.c even 3 2
350.4.j.d 4 35.l odd 12 4
448.4.i.c 2 280.bf even 6 2
448.4.i.d 2 280.bi odd 6 2
784.4.a.j 1 140.c even 2 1
784.4.a.l 1 20.d odd 2 1
882.4.a.k 1 15.d odd 2 1
882.4.a.p 1 105.g even 2 1
882.4.g.d 2 105.p even 6 2
2450.4.a.bf 1 7.b odd 2 1
2450.4.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2450))\):

\( T_{3} - 1 \)
\( T_{11} - 35 \)
\( T_{19} - 137 \)
\( T_{23} - 7 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T \)
$3$ \( 1 - T + 27 T^{2} \)
$5$ 1
$7$ 1
$11$ \( 1 - 35 T + 1331 T^{2} \)
$13$ \( 1 + 66 T + 2197 T^{2} \)
$17$ \( 1 + 59 T + 4913 T^{2} \)
$19$ \( 1 - 137 T + 6859 T^{2} \)
$23$ \( 1 - 7 T + 12167 T^{2} \)
$29$ \( 1 - 106 T + 24389 T^{2} \)
$31$ \( 1 - 75 T + 29791 T^{2} \)
$37$ \( 1 + 11 T + 50653 T^{2} \)
$41$ \( 1 + 498 T + 68921 T^{2} \)
$43$ \( 1 + 260 T + 79507 T^{2} \)
$47$ \( 1 - 171 T + 103823 T^{2} \)
$53$ \( 1 - 417 T + 148877 T^{2} \)
$59$ \( 1 + 17 T + 205379 T^{2} \)
$61$ \( 1 - 51 T + 226981 T^{2} \)
$67$ \( 1 + 439 T + 300763 T^{2} \)
$71$ \( 1 + 784 T + 357911 T^{2} \)
$73$ \( 1 + 295 T + 389017 T^{2} \)
$79$ \( 1 + 495 T + 493039 T^{2} \)
$83$ \( 1 + 932 T + 571787 T^{2} \)
$89$ \( 1 + 873 T + 704969 T^{2} \)
$97$ \( 1 - 290 T + 912673 T^{2} \)
show more
show less