Properties

Label 3525.2.a.c
Level $3525$
Weight $2$
Character orbit 3525.a
Self dual yes
Analytic conductor $28.147$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.1472667125\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 141)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} - q^{3} + 2q^{4} + 2q^{6} + 3q^{7} + q^{9} + O(q^{10}) \) \( q - 2q^{2} - q^{3} + 2q^{4} + 2q^{6} + 3q^{7} + q^{9} + q^{11} - 2q^{12} + 2q^{13} - 6q^{14} - 4q^{16} - 2q^{17} - 2q^{18} + 6q^{19} - 3q^{21} - 2q^{22} - 3q^{23} - 4q^{26} - q^{27} + 6q^{28} + 3q^{29} + 2q^{31} + 8q^{32} - q^{33} + 4q^{34} + 2q^{36} + 7q^{37} - 12q^{38} - 2q^{39} + 10q^{41} + 6q^{42} + 10q^{43} + 2q^{44} + 6q^{46} + q^{47} + 4q^{48} + 2q^{49} + 2q^{51} + 4q^{52} - 4q^{53} + 2q^{54} - 6q^{57} - 6q^{58} + 8q^{59} - 10q^{61} - 4q^{62} + 3q^{63} - 8q^{64} + 2q^{66} - 10q^{67} - 4q^{68} + 3q^{69} - 14q^{71} + 10q^{73} - 14q^{74} + 12q^{76} + 3q^{77} + 4q^{78} + 17q^{79} + q^{81} - 20q^{82} - 8q^{83} - 6q^{84} - 20q^{86} - 3q^{87} + 6q^{89} + 6q^{91} - 6q^{92} - 2q^{93} - 2q^{94} - 8q^{96} - q^{97} - 4q^{98} + q^{99} + O(q^{100}) \)

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 2.00000 0 2.00000 3.00000 0 1.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(5\) \(1\)
\(47\) \(-1\)

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 3525.2.a.c 1
5.b even 2 1 141.2.a.e 1
15.d odd 2 1 423.2.a.b 1
20.d odd 2 1 2256.2.a.e 1
35.c odd 2 1 6909.2.a.k 1
40.e odd 2 1 9024.2.a.bq 1
40.f even 2 1 9024.2.a.n 1
60.h even 2 1 6768.2.a.n 1
235.b odd 2 1 6627.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
141.2.a.e 1 5.b even 2 1
423.2.a.b 1 15.d odd 2 1
2256.2.a.e 1 20.d odd 2 1
3525.2.a.c 1 1.a even 1 1 trivial
6627.2.a.i 1 235.b odd 2 1
6768.2.a.n 1 60.h even 2 1
6909.2.a.k 1 35.c odd 2 1
9024.2.a.n 1 40.f even 2 1
9024.2.a.bq 1 40.e odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3525))\):

\( T_{2} + 2 \)
\( T_{7} - 3 \)
\( T_{11} - 1 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 2 + T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( -3 + T \)
$11$ \( -1 + T \)
$13$ \( -2 + T \)
$17$ \( 2 + T \)
$19$ \( -6 + T \)
$23$ \( 3 + T \)
$29$ \( -3 + T \)
$31$ \( -2 + T \)
$37$ \( -7 + T \)
$41$ \( -10 + T \)
$43$ \( -10 + T \)
$47$ \( -1 + T \)
$53$ \( 4 + T \)
$59$ \( -8 + T \)
$61$ \( 10 + T \)
$67$ \( 10 + T \)
$71$ \( 14 + T \)
$73$ \( -10 + T \)
$79$ \( -17 + T \)
$83$ \( 8 + T \)
$89$ \( -6 + T \)
$97$ \( 1 + T \)
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