Properties

Label 4027.2.a.c
Level 4027
Weight 2
Character orbit 4027.a
Self dual Yes
Analytic conductor 32.156
Analytic rank 0
Dimension 174
CM No

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.155756894\)
Analytic rank: \(0\)
Dimension: \(174\)
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.

\(\operatorname{Tr}(f)(q) = \) \(174q \) \(\mathstrut +\mathstrut 21q^{2} \) \(\mathstrut +\mathstrut 17q^{3} \) \(\mathstrut +\mathstrut 187q^{4} \) \(\mathstrut +\mathstrut 72q^{5} \) \(\mathstrut +\mathstrut 21q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 197q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(174q \) \(\mathstrut +\mathstrut 21q^{2} \) \(\mathstrut +\mathstrut 17q^{3} \) \(\mathstrut +\mathstrut 187q^{4} \) \(\mathstrut +\mathstrut 72q^{5} \) \(\mathstrut +\mathstrut 21q^{6} \) \(\mathstrut +\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 54q^{8} \) \(\mathstrut +\mathstrut 197q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut +\mathstrut 35q^{11} \) \(\mathstrut +\mathstrut 23q^{12} \) \(\mathstrut +\mathstrut 91q^{13} \) \(\mathstrut +\mathstrut 18q^{14} \) \(\mathstrut +\mathstrut 16q^{15} \) \(\mathstrut +\mathstrut 201q^{16} \) \(\mathstrut +\mathstrut 148q^{17} \) \(\mathstrut +\mathstrut 39q^{18} \) \(\mathstrut +\mathstrut 36q^{19} \) \(\mathstrut +\mathstrut 128q^{20} \) \(\mathstrut +\mathstrut 57q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 96q^{23} \) \(\mathstrut +\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 226q^{25} \) \(\mathstrut +\mathstrut 44q^{26} \) \(\mathstrut +\mathstrut 62q^{27} \) \(\mathstrut +\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 122q^{29} \) \(\mathstrut +\mathstrut 25q^{30} \) \(\mathstrut +\mathstrut 23q^{31} \) \(\mathstrut +\mathstrut 104q^{32} \) \(\mathstrut +\mathstrut 91q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 80q^{35} \) \(\mathstrut +\mathstrut 222q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut +\mathstrut 125q^{38} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 53q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 70q^{44} \) \(\mathstrut +\mathstrut 185q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut +\mathstrut 110q^{47} \) \(\mathstrut +\mathstrut 36q^{48} \) \(\mathstrut +\mathstrut 210q^{49} \) \(\mathstrut +\mathstrut 51q^{50} \) \(\mathstrut +\mathstrut 33q^{51} \) \(\mathstrut +\mathstrut 118q^{52} \) \(\mathstrut +\mathstrut 214q^{53} \) \(\mathstrut +\mathstrut 8q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 41q^{56} \) \(\mathstrut +\mathstrut 76q^{57} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 66q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 114q^{61} \) \(\mathstrut +\mathstrut 175q^{62} \) \(\mathstrut +\mathstrut 62q^{63} \) \(\mathstrut +\mathstrut 190q^{64} \) \(\mathstrut +\mathstrut 128q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 348q^{68} \) \(\mathstrut +\mathstrut 115q^{69} \) \(\mathstrut -\mathstrut 38q^{70} \) \(\mathstrut +\mathstrut 54q^{71} \) \(\mathstrut +\mathstrut 101q^{72} \) \(\mathstrut +\mathstrut 107q^{73} \) \(\mathstrut +\mathstrut 71q^{74} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 368q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut -\mathstrut 14q^{79} \) \(\mathstrut +\mathstrut 205q^{80} \) \(\mathstrut +\mathstrut 222q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut +\mathstrut 246q^{83} \) \(\mathstrut +\mathstrut 41q^{84} \) \(\mathstrut +\mathstrut 87q^{85} \) \(\mathstrut +\mathstrut 33q^{86} \) \(\mathstrut +\mathstrut 100q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 147q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 23q^{91} \) \(\mathstrut +\mathstrut 189q^{92} \) \(\mathstrut +\mathstrut 117q^{93} \) \(\mathstrut +\mathstrut 23q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut +\mathstrut 38q^{96} \) \(\mathstrut +\mathstrut 52q^{97} \) \(\mathstrut +\mathstrut 148q^{98} \) \(\mathstrut +\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80755 0.290452 5.88232 −1.66261 −0.815457 1.40907 −10.8998 −2.91564 4.66785
1.2 −2.72607 −2.28516 5.43147 2.07141 6.22952 −3.86589 −9.35442 2.22198 −5.64680
1.3 −2.70396 −2.87178 5.31140 4.01870 7.76519 2.72741 −8.95389 5.24714 −10.8664
1.4 −2.66961 −0.492916 5.12680 2.37281 1.31589 1.32431 −8.34733 −2.75703 −6.33447
1.5 −2.64301 3.39832 4.98550 −0.538898 −8.98178 −0.766621 −7.89070 8.54855 1.42431
1.6 −2.61961 0.347361 4.86233 3.06529 −0.909948 −2.40365 −7.49819 −2.87934 −8.02984
1.7 −2.58182 1.87364 4.66582 2.74921 −4.83740 4.58392 −6.88267 0.510512 −7.09798
1.8 −2.54479 0.596838 4.47598 4.06364 −1.51883 −0.751735 −6.30086 −2.64378 −10.3411
1.9 −2.53459 2.56413 4.42415 −2.01095 −6.49903 −2.72523 −6.14422 3.57478 5.09695
1.10 −2.51686 −1.86760 4.33456 −3.04693 4.70049 −0.421908 −5.87575 0.487938 7.66868
1.11 −2.50865 −1.26179 4.29331 −1.32725 3.16538 −1.28298 −5.75310 −1.40789 3.32960
1.12 −2.50780 2.09202 4.28906 −3.15733 −5.24636 −2.77421 −5.74049 1.37654 7.91796
1.13 −2.45988 0.0412137 4.05100 −0.833121 −0.101381 −2.59297 −5.04521 −2.99830 2.04937
1.14 −2.44690 2.58463 3.98731 2.27529 −6.32432 3.46377 −4.86273 3.68031 −5.56739
1.15 −2.41774 −1.12112 3.84547 1.14031 2.71058 1.36358 −4.46187 −1.74309 −2.75699
1.16 −2.37550 −3.14920 3.64299 0.257515 7.48091 1.36222 −3.90291 6.91744 −0.611727
1.17 −2.36541 −2.31312 3.59515 −1.08906 5.47148 −0.547834 −3.77318 2.35053 2.57606
1.18 −2.36345 0.649215 3.58591 −0.526324 −1.53439 1.65204 −3.74822 −2.57852 1.24394
1.19 −2.34379 2.27636 3.49337 1.43795 −5.33532 −0.700822 −3.50016 2.18181 −3.37027
1.20 −2.24334 −2.49753 3.03259 −3.94500 5.60282 −4.10422 −2.31645 3.23765 8.85000
See next 80 embeddings (of 174 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.174
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(4027\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{174} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4027))\).