Properties

Label 4011.2.a.j
Level 4011
Weight 2
Character orbit 4011.a
Self dual Yes
Analytic conductor 32.028
Analytic rank 0
Dimension 26
CM No

Related objects

Downloads

Learn more about

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: \(26\)
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.

\(\operatorname{Tr}(f)(q) = \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 26q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 26q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut +\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 34q^{12} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 54q^{16} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut -\mathstrut 22q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut +\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut -\mathstrut 34q^{28} \) \(\mathstrut +\mathstrut 23q^{29} \) \(\mathstrut +\mathstrut q^{30} \) \(\mathstrut +\mathstrut 18q^{31} \) \(\mathstrut +\mathstrut 10q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 34q^{36} \) \(\mathstrut +\mathstrut 23q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 14q^{40} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 60q^{44} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 54q^{48} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 19q^{52} \) \(\mathstrut +\mathstrut 31q^{53} \) \(\mathstrut +\mathstrut 41q^{55} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut +\mathstrut 19q^{58} \) \(\mathstrut -\mathstrut 2q^{59} \) \(\mathstrut +\mathstrut 22q^{60} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 35q^{62} \) \(\mathstrut -\mathstrut 26q^{63} \) \(\mathstrut +\mathstrut 132q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 17q^{66} \) \(\mathstrut +\mathstrut 47q^{67} \) \(\mathstrut -\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 3q^{69} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut +\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 23q^{73} \) \(\mathstrut +\mathstrut 34q^{74} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 72q^{76} \) \(\mathstrut -\mathstrut 13q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 21q^{80} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut +\mathstrut 60q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut +\mathstrut 34q^{84} \) \(\mathstrut +\mathstrut 36q^{85} \) \(\mathstrut +\mathstrut 21q^{86} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 67q^{88} \) \(\mathstrut +\mathstrut 14q^{89} \) \(\mathstrut -\mathstrut q^{90} \) \(\mathstrut +\mathstrut q^{91} \) \(\mathstrut +\mathstrut 20q^{92} \) \(\mathstrut -\mathstrut 18q^{93} \) \(\mathstrut +\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 4q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 48q^{97} \) \(\mathstrut +\mathstrut 13q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.79513 −1.00000 5.81272 0.438876 2.79513 −1.00000 −10.6570 1.00000 −1.22671
1.2 −2.64395 −1.00000 4.99049 −3.91233 2.64395 −1.00000 −7.90671 1.00000 10.3440
1.3 −2.56383 −1.00000 4.57324 −0.592667 2.56383 −1.00000 −6.59735 1.00000 1.51950
1.4 −2.43265 −1.00000 3.91781 2.62505 2.43265 −1.00000 −4.66537 1.00000 −6.38585
1.5 −1.95690 −1.00000 1.82947 −3.69601 1.95690 −1.00000 0.333702 1.00000 7.23273
1.6 −1.82745 −1.00000 1.33956 3.12821 1.82745 −1.00000 1.20691 1.00000 −5.71664
1.7 −1.71993 −1.00000 0.958143 2.53174 1.71993 −1.00000 1.79192 1.00000 −4.35441
1.8 −1.59694 −1.00000 0.550208 0.890069 1.59694 −1.00000 2.31523 1.00000 −1.42138
1.9 −1.07123 −1.00000 −0.852471 −1.60541 1.07123 −1.00000 3.05565 1.00000 1.71976
1.10 −1.03703 −1.00000 −0.924574 −1.10504 1.03703 −1.00000 3.03286 1.00000 1.14595
1.11 −0.713989 −1.00000 −1.49022 −2.22886 0.713989 −1.00000 2.49198 1.00000 1.59138
1.12 −0.596587 −1.00000 −1.64408 4.06129 0.596587 −1.00000 2.17401 1.00000 −2.42291
1.13 −0.163923 −1.00000 −1.97313 0.716872 0.163923 −1.00000 0.651287 1.00000 −0.117512
1.14 0.272327 −1.00000 −1.92584 −2.12381 −0.272327 −1.00000 −1.06911 1.00000 −0.578372
1.15 0.506999 −1.00000 −1.74295 3.81191 −0.506999 −1.00000 −1.89767 1.00000 1.93264
1.16 0.934309 −1.00000 −1.12707 0.782566 −0.934309 −1.00000 −2.92165 1.00000 0.731158
1.17 0.972990 −1.00000 −1.05329 4.14138 −0.972990 −1.00000 −2.97082 1.00000 4.02952
1.18 1.06777 −1.00000 −0.859868 0.128461 −1.06777 −1.00000 −3.05368 1.00000 0.137167
1.19 1.34762 −1.00000 −0.183926 −3.65993 −1.34762 −1.00000 −2.94310 1.00000 −4.93219
1.20 1.71722 −1.00000 0.948829 0.183092 −1.71722 −1.00000 −1.80509 1.00000 0.314408
See all 26 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
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 \(T_{2}^{26} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4011))\).