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
Inner twists 1

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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: \(32.1557568940\)
Analytic rank: \(0\)
Dimension: \(174\)
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.

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

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 −2.80755 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:
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 4027.2.a.c 174
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4027.2.a.c 174 1.a even 1 1 trivial

Atkin-Lehner signs

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

Hecke kernels

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