Properties

Label 3150.2.a.i
Level 3150
Weight 2
Character orbit 3150.a
Self dual Yes
Analytic conductor 25.153
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(25.1528766367\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} + 4q^{13} + q^{14} + q^{16} + 6q^{17} + 2q^{19} - 4q^{26} - q^{28} + 6q^{29} - 4q^{31} - q^{32} - 6q^{34} - 2q^{37} - 2q^{38} - 6q^{41} - 8q^{43} - 12q^{47} + q^{49} + 4q^{52} + 6q^{53} + q^{56} - 6q^{58} + 6q^{59} + 8q^{61} + 4q^{62} + q^{64} + 4q^{67} + 6q^{68} - 2q^{73} + 2q^{74} + 2q^{76} + 8q^{79} + 6q^{82} - 6q^{83} + 8q^{86} + 6q^{89} - 4q^{91} + 12q^{94} + 10q^{97} - q^{98} + O(q^{100}) \)

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

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3150))\):

\( T_{11} \)
\( T_{13} - 4 \)
\( T_{17} - 6 \)
\( T_{19} - 2 \)
\( T_{29} - 6 \)