Properties

Label 6014.2.a.i
Level 6014
Weight 2
Character orbit 6014.a
Self dual Yes
Analytic conductor 48.022
Analytic rank 0
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6014.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0220317756\)
Analytic rank: \(0\)
Dimension: \(28\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(28q \) \(\mathstrut +\mathstrut 28q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 28q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(28q \) \(\mathstrut +\mathstrut 28q^{2} \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 28q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut +\mathstrut 28q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 12q^{12} \) \(\mathstrut +\mathstrut 20q^{13} \) \(\mathstrut +\mathstrut 13q^{14} \) \(\mathstrut +\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 28q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 38q^{18} \) \(\mathstrut +\mathstrut 35q^{19} \) \(\mathstrut +\mathstrut 10q^{20} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut +\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 46q^{25} \) \(\mathstrut +\mathstrut 20q^{26} \) \(\mathstrut +\mathstrut 39q^{27} \) \(\mathstrut +\mathstrut 13q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut +\mathstrut 28q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut +\mathstrut 11q^{37} \) \(\mathstrut +\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 30q^{42} \) \(\mathstrut +\mathstrut 43q^{43} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut +\mathstrut 11q^{45} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 12q^{48} \) \(\mathstrut +\mathstrut 99q^{49} \) \(\mathstrut +\mathstrut 46q^{50} \) \(\mathstrut -\mathstrut 43q^{51} \) \(\mathstrut +\mathstrut 20q^{52} \) \(\mathstrut +\mathstrut 11q^{53} \) \(\mathstrut +\mathstrut 39q^{54} \) \(\mathstrut +\mathstrut 66q^{55} \) \(\mathstrut +\mathstrut 13q^{56} \) \(\mathstrut -\mathstrut 15q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 34q^{59} \) \(\mathstrut +\mathstrut 19q^{60} \) \(\mathstrut +\mathstrut 66q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 65q^{63} \) \(\mathstrut +\mathstrut 28q^{64} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut -\mathstrut 33q^{69} \) \(\mathstrut +\mathstrut 36q^{70} \) \(\mathstrut +\mathstrut 25q^{71} \) \(\mathstrut +\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 9q^{73} \) \(\mathstrut +\mathstrut 11q^{74} \) \(\mathstrut +\mathstrut 92q^{75} \) \(\mathstrut +\mathstrut 35q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 88q^{85} \) \(\mathstrut +\mathstrut 43q^{86} \) \(\mathstrut +\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 8q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut +\mathstrut 34q^{91} \) \(\mathstrut +\mathstrut 20q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 18q^{94} \) \(\mathstrut +\mathstrut 32q^{95} \) \(\mathstrut +\mathstrut 12q^{96} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut 99q^{98} \) \(\mathstrut +\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 1.00000 −3.13670 1.00000 −0.941618 −3.13670 −2.29539 1.00000 6.83889 −0.941618
1.2 1.00000 −2.70233 1.00000 1.19953 −2.70233 4.06202 1.00000 4.30256 1.19953
1.3 1.00000 −2.39276 1.00000 −2.51232 −2.39276 −0.441417 1.00000 2.72531 −2.51232
1.4 1.00000 −2.30582 1.00000 −2.66329 −2.30582 3.25823 1.00000 2.31680 −2.66329
1.5 1.00000 −2.09814 1.00000 3.98650 −2.09814 1.58307 1.00000 1.40217 3.98650
1.6 1.00000 −2.00278 1.00000 3.09460 −2.00278 −1.28060 1.00000 1.01112 3.09460
1.7 1.00000 −1.45310 1.00000 1.69777 −1.45310 −3.88385 1.00000 −0.888510 1.69777
1.8 1.00000 −1.17518 1.00000 −3.11669 −1.17518 −1.35191 1.00000 −1.61895 −3.11669
1.9 1.00000 −1.17506 1.00000 −0.398275 −1.17506 −4.80253 1.00000 −1.61923 −0.398275
1.10 1.00000 −0.706567 1.00000 0.802206 −0.706567 5.13557 1.00000 −2.50076 0.802206
1.11 1.00000 −0.492368 1.00000 −0.547220 −0.492368 4.87929 1.00000 −2.75757 −0.547220
1.12 1.00000 −0.370415 1.00000 2.36567 −0.370415 1.74646 1.00000 −2.86279 2.36567
1.13 1.00000 −0.289255 1.00000 −1.50320 −0.289255 −2.57965 1.00000 −2.91633 −1.50320
1.14 1.00000 0.680504 1.00000 −3.85980 0.680504 −5.17023 1.00000 −2.53691 −3.85980
1.15 1.00000 0.739140 1.00000 −1.50686 0.739140 −3.35387 1.00000 −2.45367 −1.50686
1.16 1.00000 1.28193 1.00000 1.29778 1.28193 1.61746 1.00000 −1.35667 1.29778
1.17 1.00000 1.56730 1.00000 4.16992 1.56730 1.53618 1.00000 −0.543558 4.16992
1.18 1.00000 1.69964 1.00000 3.58462 1.69964 3.25191 1.00000 −0.111231 3.58462
1.19 1.00000 1.97781 1.00000 3.20639 1.97781 −4.54964 1.00000 0.911724 3.20639
1.20 1.00000 2.05494 1.00000 −3.09222 2.05494 3.17288 1.00000 1.22280 −3.09222
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(31\) \(1\)
\(97\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{28} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\).