Properties

Label 4011.2.a.m
Level 4011
Weight 2
Character orbit 4011.a
Self dual Yes
Analytic conductor 32.028
Analytic rank 0
Dimension 29
CM No

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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: \(29\)
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.

\(\operatorname{Tr}(f)(q) = \) \(29q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut 22q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 29q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 29q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(29q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 29q^{3} \) \(\mathstrut +\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut 22q^{5} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 29q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 29q^{9} \) \(\mathstrut +\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 40q^{12} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 58q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut 52q^{20} \) \(\mathstrut -\mathstrut 29q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 36q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 57q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 29q^{27} \) \(\mathstrut -\mathstrut 40q^{28} \) \(\mathstrut +\mathstrut 20q^{29} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 46q^{32} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 40q^{36} \) \(\mathstrut +\mathstrut 22q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 26q^{41} \) \(\mathstrut -\mathstrut 6q^{42} \) \(\mathstrut +\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 22q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 28q^{46} \) \(\mathstrut +\mathstrut 41q^{47} \) \(\mathstrut +\mathstrut 58q^{48} \) \(\mathstrut +\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 17q^{51} \) \(\mathstrut +\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 37q^{53} \) \(\mathstrut +\mathstrut 6q^{54} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut +\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 52q^{60} \) \(\mathstrut +\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 59q^{64} \) \(\mathstrut +\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 17q^{66} \) \(\mathstrut +\mathstrut 30q^{67} \) \(\mathstrut +\mathstrut 33q^{68} \) \(\mathstrut +\mathstrut 36q^{69} \) \(\mathstrut +\mathstrut 68q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut +\mathstrut 21q^{74} \) \(\mathstrut +\mathstrut 57q^{75} \) \(\mathstrut +\mathstrut 11q^{76} \) \(\mathstrut -\mathstrut 11q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut +\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 110q^{80} \) \(\mathstrut +\mathstrut 29q^{81} \) \(\mathstrut -\mathstrut 49q^{82} \) \(\mathstrut +\mathstrut 13q^{83} \) \(\mathstrut -\mathstrut 40q^{84} \) \(\mathstrut +\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 35q^{86} \) \(\mathstrut +\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 61q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut +\mathstrut 86q^{92} \) \(\mathstrut +\mathstrut 6q^{93} \) \(\mathstrut -\mathstrut 19q^{94} \) \(\mathstrut +\mathstrut 25q^{95} \) \(\mathstrut +\mathstrut 46q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76452 1.00000 5.64259 4.23744 −2.76452 −1.00000 −10.0700 1.00000 −11.7145
1.2 −2.55639 1.00000 4.53513 0.170446 −2.55639 −1.00000 −6.48077 1.00000 −0.435725
1.3 −2.32184 1.00000 3.39092 1.73819 −2.32184 −1.00000 −3.22949 1.00000 −4.03578
1.4 −2.24191 1.00000 3.02615 −1.20404 −2.24191 −1.00000 −2.30052 1.00000 2.69935
1.5 −2.08804 1.00000 2.35993 −2.57813 −2.08804 −1.00000 −0.751541 1.00000 5.38324
1.6 −2.00218 1.00000 2.00873 −0.971545 −2.00218 −1.00000 −0.0174879 1.00000 1.94521
1.7 −1.96996 1.00000 1.88076 4.31773 −1.96996 −1.00000 0.234907 1.00000 −8.50578
1.8 −1.47855 1.00000 0.186109 3.98947 −1.47855 −1.00000 2.68193 1.00000 −5.89863
1.9 −1.16967 1.00000 −0.631883 0.467682 −1.16967 −1.00000 3.07842 1.00000 −0.547032
1.10 −0.657179 1.00000 −1.56812 0.753891 −0.657179 −1.00000 2.34489 1.00000 −0.495441
1.11 −0.630217 1.00000 −1.60283 −2.79883 −0.630217 −1.00000 2.27056 1.00000 1.76387
1.12 −0.359948 1.00000 −1.87044 −1.76526 −0.359948 −1.00000 1.39316 1.00000 0.635404
1.13 −0.223362 1.00000 −1.95011 1.64565 −0.223362 −1.00000 0.882304 1.00000 −0.367576
1.14 −0.220924 1.00000 −1.95119 3.22358 −0.220924 −1.00000 0.872912 1.00000 −0.712166
1.15 0.336232 1.00000 −1.88695 4.17128 0.336232 −1.00000 −1.30692 1.00000 1.40252
1.16 0.797866 1.00000 −1.36341 0.229986 0.797866 −1.00000 −2.68355 1.00000 0.183498
1.17 0.830058 1.00000 −1.31100 −1.52882 0.830058 −1.00000 −2.74832 1.00000 −1.26901
1.18 1.15914 1.00000 −0.656403 −3.68396 1.15914 −1.00000 −3.07913 1.00000 −4.27022
1.19 1.18058 1.00000 −0.606227 0.961582 1.18058 −1.00000 −3.07686 1.00000 1.13523
1.20 1.22787 1.00000 −0.492335 2.78453 1.22787 −1.00000 −3.06026 1.00000 3.41904
See all 29 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.29
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{29} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\).