Properties

Label 2450.4.a.d
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

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

\(f(q)\) \(=\) \( q - 2 q^{2} - 5 q^{3} + 4 q^{4} + 10 q^{6} - 8 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} - 5 q^{3} + 4 q^{4} + 10 q^{6} - 8 q^{8} - 2 q^{9} - 57 q^{11} - 20 q^{12} - 70 q^{13} + 16 q^{16} + 51 q^{17} + 4 q^{18} - 5 q^{19} + 114 q^{22} - 69 q^{23} + 40 q^{24} + 140 q^{26} + 145 q^{27} + 114 q^{29} - 23 q^{31} - 32 q^{32} + 285 q^{33} - 102 q^{34} - 8 q^{36} + 253 q^{37} + 10 q^{38} + 350 q^{39} + 42 q^{41} + 124 q^{43} - 228 q^{44} + 138 q^{46} + 201 q^{47} - 80 q^{48} - 255 q^{51} - 280 q^{52} + 393 q^{53} - 290 q^{54} + 25 q^{57} - 228 q^{58} - 219 q^{59} + 709 q^{61} + 46 q^{62} + 64 q^{64} - 570 q^{66} - 419 q^{67} + 204 q^{68} + 345 q^{69} - 96 q^{71} + 16 q^{72} - 313 q^{73} - 506 q^{74} - 20 q^{76} - 700 q^{78} + 461 q^{79} - 671 q^{81} - 84 q^{82} - 588 q^{83} - 248 q^{86} - 570 q^{87} + 456 q^{88} + 1017 q^{89} - 276 q^{92} + 115 q^{93} - 402 q^{94} + 160 q^{96} - 1834 q^{97} + 114 q^{99}+O(q^{100}) \) 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 −5.00000 4.00000 0 10.0000 0 −8.00000 −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 2450.4.a.d 1
5.b even 2 1 98.4.a.f 1
7.b odd 2 1 2450.4.a.q 1
7.d odd 6 2 350.4.e.e 2
15.d odd 2 1 882.4.a.c 1
20.d odd 2 1 784.4.a.c 1
35.c odd 2 1 98.4.a.d 1
35.i odd 6 2 14.4.c.a 2
35.j even 6 2 98.4.c.a 2
35.k even 12 4 350.4.j.b 4
105.g even 2 1 882.4.a.f 1
105.o odd 6 2 882.4.g.u 2
105.p even 6 2 126.4.g.d 2
140.c even 2 1 784.4.a.p 1
140.s even 6 2 112.4.i.a 2
280.ba even 6 2 448.4.i.e 2
280.bk odd 6 2 448.4.i.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.c.a 2 35.i odd 6 2
98.4.a.d 1 35.c odd 2 1
98.4.a.f 1 5.b even 2 1
98.4.c.a 2 35.j even 6 2
112.4.i.a 2 140.s even 6 2
126.4.g.d 2 105.p even 6 2
350.4.e.e 2 7.d odd 6 2
350.4.j.b 4 35.k even 12 4
448.4.i.b 2 280.bk odd 6 2
448.4.i.e 2 280.ba even 6 2
784.4.a.c 1 20.d odd 2 1
784.4.a.p 1 140.c even 2 1
882.4.a.c 1 15.d odd 2 1
882.4.a.f 1 105.g even 2 1
882.4.g.u 2 105.o odd 6 2
2450.4.a.d 1 1.a even 1 1 trivial
2450.4.a.q 1 7.b odd 2 1

Hecke kernels

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

\( T_{3} + 5 \) Copy content Toggle raw display
\( T_{11} + 57 \) Copy content Toggle raw display
\( T_{19} + 5 \) Copy content Toggle raw display
\( T_{23} + 69 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T + 5 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 57 \) Copy content Toggle raw display
$13$ \( T + 70 \) Copy content Toggle raw display
$17$ \( T - 51 \) Copy content Toggle raw display
$19$ \( T + 5 \) Copy content Toggle raw display
$23$ \( T + 69 \) Copy content Toggle raw display
$29$ \( T - 114 \) Copy content Toggle raw display
$31$ \( T + 23 \) Copy content Toggle raw display
$37$ \( T - 253 \) Copy content Toggle raw display
$41$ \( T - 42 \) Copy content Toggle raw display
$43$ \( T - 124 \) Copy content Toggle raw display
$47$ \( T - 201 \) Copy content Toggle raw display
$53$ \( T - 393 \) Copy content Toggle raw display
$59$ \( T + 219 \) Copy content Toggle raw display
$61$ \( T - 709 \) Copy content Toggle raw display
$67$ \( T + 419 \) Copy content Toggle raw display
$71$ \( T + 96 \) Copy content Toggle raw display
$73$ \( T + 313 \) Copy content Toggle raw display
$79$ \( T - 461 \) Copy content Toggle raw display
$83$ \( T + 588 \) Copy content Toggle raw display
$89$ \( T - 1017 \) Copy content Toggle raw display
$97$ \( T + 1834 \) Copy content Toggle raw display
show more
show less