Properties

Label 12.4.a.a
Level 12
Weight 4
Character orbit 12.a
Self dual Yes
Analytic conductor 0.708
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 12.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.708022920069\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 36q^{11} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 54q^{15} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 100q^{19} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 72q^{23} \) \(\mathstrut +\mathstrut 199q^{25} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 234q^{29} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 108q^{33} \) \(\mathstrut -\mathstrut 144q^{35} \) \(\mathstrut -\mathstrut 226q^{37} \) \(\mathstrut -\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 90q^{41} \) \(\mathstrut +\mathstrut 452q^{43} \) \(\mathstrut -\mathstrut 162q^{45} \) \(\mathstrut +\mathstrut 432q^{47} \) \(\mathstrut -\mathstrut 279q^{49} \) \(\mathstrut +\mathstrut 54q^{51} \) \(\mathstrut +\mathstrut 414q^{53} \) \(\mathstrut -\mathstrut 648q^{55} \) \(\mathstrut -\mathstrut 300q^{57} \) \(\mathstrut -\mathstrut 684q^{59} \) \(\mathstrut +\mathstrut 422q^{61} \) \(\mathstrut +\mathstrut 72q^{63} \) \(\mathstrut +\mathstrut 180q^{65} \) \(\mathstrut +\mathstrut 332q^{67} \) \(\mathstrut +\mathstrut 216q^{69} \) \(\mathstrut -\mathstrut 360q^{71} \) \(\mathstrut +\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 597q^{75} \) \(\mathstrut +\mathstrut 288q^{77} \) \(\mathstrut +\mathstrut 512q^{79} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 1188q^{83} \) \(\mathstrut -\mathstrut 324q^{85} \) \(\mathstrut -\mathstrut 702q^{87} \) \(\mathstrut -\mathstrut 630q^{89} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut -\mathstrut 48q^{93} \) \(\mathstrut +\mathstrut 1800q^{95} \) \(\mathstrut -\mathstrut 1054q^{97} \) \(\mathstrut +\mathstrut 324q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 3.00000 0 −18.0000 0 8.00000 0 9.00000 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
\(2\) \(-1\)
\(3\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(\Gamma_0(12))\).