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Properties

Label 1.12.a.a
Level 1
Weight 12
Character orbit 1.a
Self dual Yes
Analytic conductor 0.768
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 1.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.76834318056\)
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

\(f(q)\) \(=\) \( q - 24q^{2} + 252q^{3} - 1472q^{4} + 4830q^{5} - 6048q^{6} - 16744q^{7} + 84480q^{8} - 113643q^{9} + O(q^{10}) \) \( q - 24q^{2} + 252q^{3} - 1472q^{4} + 4830q^{5} - 6048q^{6} - 16744q^{7} + 84480q^{8} - 113643q^{9} - 115920q^{10} + 534612q^{11} - 370944q^{12} - 577738q^{13} + 401856q^{14} + 1217160q^{15} + 987136q^{16} - 6905934q^{17} + 2727432q^{18} + 10661420q^{19} - 7109760q^{20} - 4219488q^{21} - 12830688q^{22} + 18643272q^{23} + 21288960q^{24} - 25499225q^{25} + 13865712q^{26} - 73279080q^{27} + 24647168q^{28} + 128406630q^{29} - 29211840q^{30} - 52843168q^{31} - 196706304q^{32} + 134722224q^{33} + 165742416q^{34} - 80873520q^{35} + 167282496q^{36} - 182213314q^{37} - 255874080q^{38} - 145589976q^{39} + 408038400q^{40} + 308120442q^{41} + 101267712q^{42} - 17125708q^{43} - 786948864q^{44} - 548895690q^{45} - 447438528q^{46} + 2687348496q^{47} + 248758272q^{48} - 1696965207q^{49} + 611981400q^{50} - 1740295368q^{51} + 850430336q^{52} - 1596055698q^{53} + 1758697920q^{54} + 2582175960q^{55} - 1414533120q^{56} + 2686677840q^{57} - 3081759120q^{58} - 5189203740q^{59} - 1791659520q^{60} + 6956478662q^{61} + 1268236032q^{62} + 1902838392q^{63} + 2699296768q^{64} - 2790474540q^{65} - 3233333376q^{66} - 15481826884q^{67} + 10165534848q^{68} + 4698104544q^{69} + 1940964480q^{70} + 9791485272q^{71} - 9600560640q^{72} + 1463791322q^{73} + 4373119536q^{74} - 6425804700q^{75} - 15693610240q^{76} - 8951543328q^{77} + 3494159424q^{78} + 38116845680q^{79} + 4767866880q^{80} + 1665188361q^{81} - 7394890608q^{82} - 29335099668q^{83} + 6211086336q^{84} - 33355661220q^{85} + 411016992q^{86} + 32358470760q^{87} + 45164021760q^{88} - 24992917110q^{89} + 13173496560q^{90} + 9673645072q^{91} - 27442896384q^{92} - 13316478336q^{93} - 64496363904q^{94} + 51494658600q^{95} - 49569988608q^{96} + 75013568546q^{97} + 40727164968q^{98} - 60754911516q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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
−24.0000 252.000 −1472.00 4830.00 −6048.00 −16744.0 84480.0 −113643. −115920.
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Hecke kernels

There are no other newforms in \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\).