Properties

Label 308.2.a.a
Level 308
Weight 2
Character orbit 308.a
Self dual Yes
Analytic conductor 2.459
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 308.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.45939238226\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q - q^{3} - q^{5} - q^{7} - 2q^{9} + O(q^{10}) \) \( q - q^{3} - q^{5} - q^{7} - 2q^{9} + q^{11} - 4q^{13} + q^{15} - 6q^{17} - 2q^{19} + q^{21} + q^{23} - 4q^{25} + 5q^{27} + 2q^{29} - q^{31} - q^{33} + q^{35} - 9q^{37} + 4q^{39} + 6q^{41} + 8q^{43} + 2q^{45} - 8q^{47} + q^{49} + 6q^{51} + 10q^{53} - q^{55} + 2q^{57} + q^{59} - 2q^{61} + 2q^{63} + 4q^{65} + 11q^{67} - q^{69} + 11q^{71} - 14q^{73} + 4q^{75} - q^{77} - 14q^{79} + q^{81} + 4q^{83} + 6q^{85} - 2q^{87} + 13q^{89} + 4q^{91} + q^{93} + 2q^{95} - 9q^{97} - 2q^{99} + O(q^{100}) \)

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
0 −1.00000 0 −1.00000 0 −1.00000 0 −2.00000 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
\(2\) \(-1\)
\(7\) \(1\)
\(11\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} + 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(308))\).