Properties

Label 630.2.a.e
Level 630
Weight 2
Character orbit 630.a
Self dual Yes
Analytic conductor 5.031
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(5.03057532734\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - 4q^{11} + 6q^{13} + q^{14} + q^{16} + 4q^{17} + 6q^{19} + q^{20} + 4q^{22} + q^{25} - 6q^{26} - q^{28} - 6q^{29} - 4q^{31} - q^{32} - 4q^{34} - q^{35} + 8q^{37} - 6q^{38} - q^{40} + 10q^{41} - 2q^{43} - 4q^{44} + 10q^{47} + q^{49} - q^{50} + 6q^{52} + 14q^{53} - 4q^{55} + q^{56} + 6q^{58} - 4q^{59} - 8q^{61} + 4q^{62} + q^{64} + 6q^{65} + 6q^{67} + 4q^{68} + q^{70} - 2q^{71} - 10q^{73} - 8q^{74} + 6q^{76} + 4q^{77} + 16q^{79} + q^{80} - 10q^{82} - 8q^{83} + 4q^{85} + 2q^{86} + 4q^{88} + 2q^{89} - 6q^{91} - 10q^{94} + 6q^{95} + 2q^{97} - q^{98} + O(q^{100}) \)

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 1.00000 0 −1.00000 −1.00000 0 −1.00000
\(n\): 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
\(2\) \(1\)
\(3\) \(1\)
\(5\) \(-1\)
\(7\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(630))\):

\( T_{11} + 4 \)
\( T_{13} - 6 \)
\( T_{17} - 4 \)
\( T_{19} - 6 \)
\( T_{29} + 6 \)