Properties

Label 245.4.a.c
Level $245$
Weight $4$
Character orbit 245.a
Self dual yes
Analytic conductor $14.455$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4554679514\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 6 q^{3} - 7 q^{4} - 5 q^{5} + 6 q^{6} - 15 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + 6 q^{3} - 7 q^{4} - 5 q^{5} + 6 q^{6} - 15 q^{8} + 9 q^{9} - 5 q^{10} - 44 q^{11} - 42 q^{12} + 6 q^{13} - 30 q^{15} + 41 q^{16} - 24 q^{17} + 9 q^{18} - 114 q^{19} + 35 q^{20} - 44 q^{22} - 52 q^{23} - 90 q^{24} + 25 q^{25} + 6 q^{26} - 108 q^{27} + 146 q^{29} - 30 q^{30} - 276 q^{31} + 161 q^{32} - 264 q^{33} - 24 q^{34} - 63 q^{36} - 210 q^{37} - 114 q^{38} + 36 q^{39} + 75 q^{40} + 444 q^{41} + 492 q^{43} + 308 q^{44} - 45 q^{45} - 52 q^{46} - 612 q^{47} + 246 q^{48} + 25 q^{50} - 144 q^{51} - 42 q^{52} + 50 q^{53} - 108 q^{54} + 220 q^{55} - 684 q^{57} + 146 q^{58} + 294 q^{59} + 210 q^{60} + 450 q^{61} - 276 q^{62} - 167 q^{64} - 30 q^{65} - 264 q^{66} - 668 q^{67} + 168 q^{68} - 312 q^{69} - 308 q^{71} - 135 q^{72} + 12 q^{73} - 210 q^{74} + 150 q^{75} + 798 q^{76} + 36 q^{78} + 596 q^{79} - 205 q^{80} - 891 q^{81} + 444 q^{82} - 966 q^{83} + 120 q^{85} + 492 q^{86} + 876 q^{87} + 660 q^{88} - 408 q^{89} - 45 q^{90} + 364 q^{92} - 1656 q^{93} - 612 q^{94} + 570 q^{95} + 966 q^{96} - 1200 q^{97} - 396 q^{99}+O(q^{100}) \) 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
1.00000 6.00000 −7.00000 −5.00000 6.00000 0 −15.0000 9.00000 −5.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)

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 245.4.a.c yes 1
3.b odd 2 1 2205.4.a.n 1
5.b even 2 1 1225.4.a.f 1
7.b odd 2 1 245.4.a.b 1
7.c even 3 2 245.4.e.c 2
7.d odd 6 2 245.4.e.d 2
21.c even 2 1 2205.4.a.k 1
35.c odd 2 1 1225.4.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
245.4.a.b 1 7.b odd 2 1
245.4.a.c yes 1 1.a even 1 1 trivial
245.4.e.c 2 7.c even 3 2
245.4.e.d 2 7.d odd 6 2
1225.4.a.f 1 5.b even 2 1
1225.4.a.g 1 35.c odd 2 1
2205.4.a.k 1 21.c even 2 1
2205.4.a.n 1 3.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(245))\):

\( T_{2} - 1 \) Copy content Toggle raw display
\( T_{3} - 6 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T - 6 \) Copy content Toggle raw display
$5$ \( T + 5 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T + 44 \) Copy content Toggle raw display
$13$ \( T - 6 \) Copy content Toggle raw display
$17$ \( T + 24 \) Copy content Toggle raw display
$19$ \( T + 114 \) Copy content Toggle raw display
$23$ \( T + 52 \) Copy content Toggle raw display
$29$ \( T - 146 \) Copy content Toggle raw display
$31$ \( T + 276 \) Copy content Toggle raw display
$37$ \( T + 210 \) Copy content Toggle raw display
$41$ \( T - 444 \) Copy content Toggle raw display
$43$ \( T - 492 \) Copy content Toggle raw display
$47$ \( T + 612 \) Copy content Toggle raw display
$53$ \( T - 50 \) Copy content Toggle raw display
$59$ \( T - 294 \) Copy content Toggle raw display
$61$ \( T - 450 \) Copy content Toggle raw display
$67$ \( T + 668 \) Copy content Toggle raw display
$71$ \( T + 308 \) Copy content Toggle raw display
$73$ \( T - 12 \) Copy content Toggle raw display
$79$ \( T - 596 \) Copy content Toggle raw display
$83$ \( T + 966 \) Copy content Toggle raw display
$89$ \( T + 408 \) Copy content Toggle raw display
$97$ \( T + 1200 \) Copy content Toggle raw display
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