Properties

Label 2450.4.a.bn
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 70)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{2} + 7 q^{3} + 4 q^{4} + 14 q^{6} + 8 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} + 7 q^{3} + 4 q^{4} + 14 q^{6} + 8 q^{8} + 22 q^{9} - 37 q^{11} + 28 q^{12} - 51 q^{13} + 16 q^{16} - 41 q^{17} + 44 q^{18} + 108 q^{19} - 74 q^{22} - 70 q^{23} + 56 q^{24} - 102 q^{26} - 35 q^{27} - 249 q^{29} + 134 q^{31} + 32 q^{32} - 259 q^{33} - 82 q^{34} + 88 q^{36} - 334 q^{37} + 216 q^{38} - 357 q^{39} - 206 q^{41} - 376 q^{43} - 148 q^{44} - 140 q^{46} + 287 q^{47} + 112 q^{48} - 287 q^{51} - 204 q^{52} - 6 q^{53} - 70 q^{54} + 756 q^{57} - 498 q^{58} + 2 q^{59} + 940 q^{61} + 268 q^{62} + 64 q^{64} - 518 q^{66} + 106 q^{67} - 164 q^{68} - 490 q^{69} + 456 q^{71} + 176 q^{72} - 650 q^{73} - 668 q^{74} + 432 q^{76} - 714 q^{78} - 1239 q^{79} - 839 q^{81} - 412 q^{82} - 428 q^{83} - 752 q^{86} - 1743 q^{87} - 296 q^{88} + 220 q^{89} - 280 q^{92} + 938 q^{93} + 574 q^{94} + 224 q^{96} + 1055 q^{97} - 814 q^{99}+O(q^{100}) \) 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
2.00000 7.00000 4.00000 0 14.0000 0 8.00000 22.0000 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.bn 1
5.b even 2 1 2450.4.a.c 1
5.c odd 4 2 490.4.c.a 2
7.b odd 2 1 350.4.a.m 1
35.c odd 2 1 350.4.a.i 1
35.f even 4 2 70.4.c.a 2
105.k odd 4 2 630.4.g.a 2
140.j odd 4 2 560.4.g.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.4.c.a 2 35.f even 4 2
350.4.a.i 1 35.c odd 2 1
350.4.a.m 1 7.b odd 2 1
490.4.c.a 2 5.c odd 4 2
560.4.g.c 2 140.j odd 4 2
630.4.g.a 2 105.k odd 4 2
2450.4.a.c 1 5.b even 2 1
2450.4.a.bn 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2450))\):

\( T_{3} - 7 \) Copy content Toggle raw display
\( T_{11} + 37 \) Copy content Toggle raw display
\( T_{19} - 108 \) Copy content Toggle raw display
\( T_{23} + 70 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) Copy content Toggle raw display
$3$ \( T - 7 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 37 \) Copy content Toggle raw display
$13$ \( T + 51 \) Copy content Toggle raw display
$17$ \( T + 41 \) Copy content Toggle raw display
$19$ \( T - 108 \) Copy content Toggle raw display
$23$ \( T + 70 \) Copy content Toggle raw display
$29$ \( T + 249 \) Copy content Toggle raw display
$31$ \( T - 134 \) Copy content Toggle raw display
$37$ \( T + 334 \) Copy content Toggle raw display
$41$ \( T + 206 \) Copy content Toggle raw display
$43$ \( T + 376 \) Copy content Toggle raw display
$47$ \( T - 287 \) Copy content Toggle raw display
$53$ \( T + 6 \) Copy content Toggle raw display
$59$ \( T - 2 \) Copy content Toggle raw display
$61$ \( T - 940 \) Copy content Toggle raw display
$67$ \( T - 106 \) Copy content Toggle raw display
$71$ \( T - 456 \) Copy content Toggle raw display
$73$ \( T + 650 \) Copy content Toggle raw display
$79$ \( T + 1239 \) Copy content Toggle raw display
$83$ \( T + 428 \) Copy content Toggle raw display
$89$ \( T - 220 \) Copy content Toggle raw display
$97$ \( T - 1055 \) Copy content Toggle raw display
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