Properties

Label 2450.4.a.bf
Level $2450$
Weight $4$
Character orbit 2450.a
Self dual yes
Analytic conductor $144.555$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q + 2 q^{2} - q^{3} + 4 q^{4} - 2 q^{6} + 8 q^{8} - 26 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{2} - q^{3} + 4 q^{4} - 2 q^{6} + 8 q^{8} - 26 q^{9} + 35 q^{11} - 4 q^{12} + 66 q^{13} + 16 q^{16} + 59 q^{17} - 52 q^{18} - 137 q^{19} + 70 q^{22} + 7 q^{23} - 8 q^{24} + 132 q^{26} + 53 q^{27} + 106 q^{29} - 75 q^{31} + 32 q^{32} - 35 q^{33} + 118 q^{34} - 104 q^{36} - 11 q^{37} - 274 q^{38} - 66 q^{39} + 498 q^{41} - 260 q^{43} + 140 q^{44} + 14 q^{46} - 171 q^{47} - 16 q^{48} - 59 q^{51} + 264 q^{52} + 417 q^{53} + 106 q^{54} + 137 q^{57} + 212 q^{58} + 17 q^{59} - 51 q^{61} - 150 q^{62} + 64 q^{64} - 70 q^{66} - 439 q^{67} + 236 q^{68} - 7 q^{69} - 784 q^{71} - 208 q^{72} + 295 q^{73} - 22 q^{74} - 548 q^{76} - 132 q^{78} - 495 q^{79} + 649 q^{81} + 996 q^{82} + 932 q^{83} - 520 q^{86} - 106 q^{87} + 280 q^{88} + 873 q^{89} + 28 q^{92} + 75 q^{93} - 342 q^{94} - 32 q^{96} - 290 q^{97} - 910 q^{99}+O(q^{100}) \) 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 −1.00000 4.00000 0 −2.00000 0 8.00000 −26.0000 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.bf 1
5.b even 2 1 98.4.a.c 1
7.b odd 2 1 2450.4.a.bh 1
7.d odd 6 2 350.4.e.b 2
15.d odd 2 1 882.4.a.p 1
20.d odd 2 1 784.4.a.j 1
35.c odd 2 1 98.4.a.b 1
35.i odd 6 2 14.4.c.b 2
35.j even 6 2 98.4.c.e 2
35.k even 12 4 350.4.j.d 4
105.g even 2 1 882.4.a.k 1
105.o odd 6 2 882.4.g.d 2
105.p even 6 2 126.4.g.c 2
140.c even 2 1 784.4.a.l 1
140.s even 6 2 112.4.i.b 2
280.ba even 6 2 448.4.i.d 2
280.bk odd 6 2 448.4.i.c 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
14.4.c.b 2 35.i odd 6 2
98.4.a.b 1 35.c odd 2 1
98.4.a.c 1 5.b even 2 1
98.4.c.e 2 35.j even 6 2
112.4.i.b 2 140.s even 6 2
126.4.g.c 2 105.p even 6 2
350.4.e.b 2 7.d odd 6 2
350.4.j.d 4 35.k even 12 4
448.4.i.c 2 280.bk odd 6 2
448.4.i.d 2 280.ba even 6 2
784.4.a.j 1 20.d odd 2 1
784.4.a.l 1 140.c even 2 1
882.4.a.k 1 105.g even 2 1
882.4.a.p 1 15.d odd 2 1
882.4.g.d 2 105.o odd 6 2
2450.4.a.bf 1 1.a even 1 1 trivial
2450.4.a.bh 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 \(S_{4}^{\mathrm{new}}(\Gamma_0(2450))\):

\( T_{3} + 1 \) Copy content Toggle raw display
\( T_{11} - 35 \) Copy content Toggle raw display
\( T_{19} + 137 \) Copy content Toggle raw display
\( T_{23} - 7 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 2 \) 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
$11$ \( T - 35 \) Copy content Toggle raw display
$13$ \( T - 66 \) Copy content Toggle raw display
$17$ \( T - 59 \) Copy content Toggle raw display
$19$ \( T + 137 \) Copy content Toggle raw display
$23$ \( T - 7 \) Copy content Toggle raw display
$29$ \( T - 106 \) Copy content Toggle raw display
$31$ \( T + 75 \) Copy content Toggle raw display
$37$ \( T + 11 \) Copy content Toggle raw display
$41$ \( T - 498 \) Copy content Toggle raw display
$43$ \( T + 260 \) Copy content Toggle raw display
$47$ \( T + 171 \) Copy content Toggle raw display
$53$ \( T - 417 \) Copy content Toggle raw display
$59$ \( T - 17 \) Copy content Toggle raw display
$61$ \( T + 51 \) Copy content Toggle raw display
$67$ \( T + 439 \) Copy content Toggle raw display
$71$ \( T + 784 \) Copy content Toggle raw display
$73$ \( T - 295 \) Copy content Toggle raw display
$79$ \( T + 495 \) Copy content Toggle raw display
$83$ \( T - 932 \) Copy content Toggle raw display
$89$ \( T - 873 \) Copy content Toggle raw display
$97$ \( T + 290 \) Copy content Toggle raw display
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