Properties

Label 4025.2.a.f
Level 4025
Weight 2
Character orbit 4025.a
Self dual Yes
Analytic conductor 32.140
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + q^{7} - 3q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} - q^{4} + q^{7} - 3q^{8} - 3q^{9} - 4q^{11} + 2q^{13} + q^{14} - q^{16} - 6q^{17} - 3q^{18} + 4q^{19} - 4q^{22} - q^{23} + 2q^{26} - q^{28} - 2q^{29} + 4q^{31} + 5q^{32} - 6q^{34} + 3q^{36} + 10q^{37} + 4q^{38} + 10q^{41} - 12q^{43} + 4q^{44} - q^{46} + 12q^{47} + q^{49} - 2q^{52} - 14q^{53} - 3q^{56} - 2q^{58} + 8q^{59} + 10q^{61} + 4q^{62} - 3q^{63} + 7q^{64} + 4q^{67} + 6q^{68} + 8q^{71} + 9q^{72} + 6q^{73} + 10q^{74} - 4q^{76} - 4q^{77} + 9q^{81} + 10q^{82} - 12q^{83} - 12q^{86} + 12q^{88} - 2q^{89} + 2q^{91} + q^{92} + 12q^{94} + 2q^{97} + q^{98} + 12q^{99} + O(q^{100}) \)

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

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(7\) \(-1\)
\(23\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\):

\( T_{2} - 1 \)
\( T_{3} \)
\( T_{11} + 4 \)