Properties

Label 4.12.a.a
Level 4
Weight 12
Character orbit 4.a
Self dual Yes
Analytic conductor 3.073
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(3.07337272224\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 516q^{3} \) \(\mathstrut -\mathstrut 10530q^{5} \) \(\mathstrut +\mathstrut 49304q^{7} \) \(\mathstrut +\mathstrut 89109q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 516q^{3} \) \(\mathstrut -\mathstrut 10530q^{5} \) \(\mathstrut +\mathstrut 49304q^{7} \) \(\mathstrut +\mathstrut 89109q^{9} \) \(\mathstrut -\mathstrut 309420q^{11} \) \(\mathstrut -\mathstrut 1723594q^{13} \) \(\mathstrut +\mathstrut 5433480q^{15} \) \(\mathstrut -\mathstrut 2279502q^{17} \) \(\mathstrut +\mathstrut 4550444q^{19} \) \(\mathstrut -\mathstrut 25440864q^{21} \) \(\mathstrut -\mathstrut 7282872q^{23} \) \(\mathstrut +\mathstrut 62052775q^{25} \) \(\mathstrut +\mathstrut 45427608q^{27} \) \(\mathstrut -\mathstrut 69040026q^{29} \) \(\mathstrut -\mathstrut 141740704q^{31} \) \(\mathstrut +\mathstrut 159660720q^{33} \) \(\mathstrut -\mathstrut 519171120q^{35} \) \(\mathstrut +\mathstrut 711366974q^{37} \) \(\mathstrut +\mathstrut 889374504q^{39} \) \(\mathstrut -\mathstrut 1225262214q^{41} \) \(\mathstrut -\mathstrut 33606220q^{43} \) \(\mathstrut -\mathstrut 938317770q^{45} \) \(\mathstrut +\mathstrut 123214608q^{47} \) \(\mathstrut +\mathstrut 453557673q^{49} \) \(\mathstrut +\mathstrut 1176223032q^{51} \) \(\mathstrut +\mathstrut 1106121582q^{53} \) \(\mathstrut +\mathstrut 3258192600q^{55} \) \(\mathstrut -\mathstrut 2348029104q^{57} \) \(\mathstrut -\mathstrut 9062779932q^{59} \) \(\mathstrut -\mathstrut 3854150458q^{61} \) \(\mathstrut +\mathstrut 4393430136q^{63} \) \(\mathstrut +\mathstrut 18149444820q^{65} \) \(\mathstrut -\mathstrut 15313764676q^{67} \) \(\mathstrut +\mathstrut 3757961952q^{69} \) \(\mathstrut +\mathstrut 20619626328q^{71} \) \(\mathstrut -\mathstrut 2063718694q^{73} \) \(\mathstrut -\mathstrut 32019231900q^{75} \) \(\mathstrut -\mathstrut 15255643680q^{77} \) \(\mathstrut +\mathstrut 13689871472q^{79} \) \(\mathstrut -\mathstrut 39226037751q^{81} \) \(\mathstrut +\mathstrut 65570428908q^{83} \) \(\mathstrut +\mathstrut 24003156060q^{85} \) \(\mathstrut +\mathstrut 35624653416q^{87} \) \(\mathstrut -\mathstrut 29715508854q^{89} \) \(\mathstrut -\mathstrut 84980078576q^{91} \) \(\mathstrut +\mathstrut 73138203264q^{93} \) \(\mathstrut -\mathstrut 47916175320q^{95} \) \(\mathstrut -\mathstrut 23439626206q^{97} \) \(\mathstrut -\mathstrut 27572106780q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −516.000 0 −10530.0 0 49304.0 0 89109.0 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
\(2\) \(-1\)

Hecke kernels

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