Properties

Label 4011.2.a.k
Level 4011
Weight 2
Character orbit 4011.a
Self dual yes
Analytic conductor 32.028
Analytic rank 0
Dimension 27
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4011 = 3 \cdot 7 \cdot 191 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4011.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0279962507\)
Analytic rank: \(0\)
Dimension: \(27\)
Coefficient ring index: multiple of None
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 27q + 9q^{2} + 27q^{3} + 31q^{4} + 23q^{5} + 9q^{6} + 27q^{7} + 18q^{8} + 27q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 27q + 9q^{2} + 27q^{3} + 31q^{4} + 23q^{5} + 9q^{6} + 27q^{7} + 18q^{8} + 27q^{9} + 10q^{10} + 22q^{11} + 31q^{12} + 15q^{13} + 9q^{14} + 23q^{15} + 39q^{16} + 22q^{17} + 9q^{18} + 24q^{19} + 46q^{20} + 27q^{21} - 19q^{22} + 36q^{23} + 18q^{24} + 38q^{25} + 19q^{26} + 27q^{27} + 31q^{28} + 32q^{29} + 10q^{30} + 11q^{31} + 15q^{32} + 22q^{33} - 4q^{34} + 23q^{35} + 31q^{36} + 6q^{37} + 8q^{38} + 15q^{39} + 16q^{41} + 9q^{42} - 11q^{43} + 22q^{44} + 23q^{45} - 56q^{46} + 39q^{47} + 39q^{48} + 27q^{49} - 7q^{50} + 22q^{51} + 10q^{52} + 24q^{53} + 9q^{54} + 16q^{55} + 18q^{56} + 24q^{57} - 31q^{58} + 31q^{59} + 46q^{60} + 28q^{61} - 4q^{62} + 27q^{63} + 40q^{64} + 33q^{65} - 19q^{66} - 7q^{67} + 25q^{68} + 36q^{69} + 10q^{70} + 49q^{71} + 18q^{72} - 13q^{73} + 7q^{74} + 38q^{75} + 15q^{76} + 22q^{77} + 19q^{78} - 18q^{79} + 78q^{80} + 27q^{81} + 31q^{82} + 59q^{83} + 31q^{84} - 20q^{85} + 35q^{86} + 32q^{87} - 49q^{88} + 49q^{89} + 10q^{90} + 15q^{91} + 52q^{92} + 11q^{93} + 17q^{94} + 38q^{95} + 15q^{96} - 7q^{97} + 9q^{98} + 22q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.65342 1.00000 5.04066 4.09935 −2.65342 1.00000 −8.06816 1.00000 −10.8773
1.2 −2.52420 1.00000 4.37157 −0.338133 −2.52420 1.00000 −5.98631 1.00000 0.853514
1.3 −2.42203 1.00000 3.86625 1.50568 −2.42203 1.00000 −4.52011 1.00000 −3.64681
1.4 −1.70789 1.00000 0.916895 2.36693 −1.70789 1.00000 1.84983 1.00000 −4.04246
1.5 −1.69492 1.00000 0.872752 −3.19478 −1.69492 1.00000 1.91059 1.00000 5.41490
1.6 −1.64011 1.00000 0.689959 −1.40502 −1.64011 1.00000 2.14861 1.00000 2.30438
1.7 −1.28891 1.00000 −0.338712 0.716613 −1.28891 1.00000 3.01439 1.00000 −0.923650
1.8 −1.05296 1.00000 −0.891266 4.03535 −1.05296 1.00000 3.04440 1.00000 −4.24908
1.9 −0.768548 1.00000 −1.40933 3.25090 −0.768548 1.00000 2.62024 1.00000 −2.49847
1.10 −0.667457 1.00000 −1.55450 −3.08787 −0.667457 1.00000 2.37248 1.00000 2.06102
1.11 −0.105370 1.00000 −1.98890 −1.28706 −0.105370 1.00000 0.420311 1.00000 0.135618
1.12 −0.0599798 1.00000 −1.99640 3.32796 −0.0599798 1.00000 0.239704 1.00000 −0.199610
1.13 0.267433 1.00000 −1.92848 0.0366447 0.267433 1.00000 −1.05060 1.00000 0.00980000
1.14 0.374739 1.00000 −1.85957 2.21215 0.374739 1.00000 −1.44633 1.00000 0.828982
1.15 0.640778 1.00000 −1.58940 −2.69509 0.640778 1.00000 −2.30001 1.00000 −1.72696
1.16 1.25182 1.00000 −0.432954 2.68317 1.25182 1.00000 −3.04561 1.00000 3.35884
1.17 1.25557 1.00000 −0.423542 3.43059 1.25557 1.00000 −3.04293 1.00000 4.30735
1.18 1.40876 1.00000 −0.0154013 −2.50452 1.40876 1.00000 −2.83921 1.00000 −3.52826
1.19 1.44666 1.00000 0.0928390 2.29705 1.44666 1.00000 −2.75902 1.00000 3.32306
1.20 1.74433 1.00000 1.04268 −1.87140 1.74433 1.00000 −1.66989 1.00000 −3.26434
See all 27 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.27
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4011.2.a.k 27
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4011.2.a.k 27 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(191\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{27} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\).