Properties

Label 4015.2.a.i
Level 4015
Weight 2
Character orbit 4015.a
Self dual yes
Analytic conductor 32.060
Analytic rank 0
Dimension 38
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(38\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 38q + 4q^{2} + 5q^{3} + 50q^{4} + 38q^{5} + 11q^{6} + 15q^{8} + 63q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 38q + 4q^{2} + 5q^{3} + 50q^{4} + 38q^{5} + 11q^{6} + 15q^{8} + 63q^{9} + 4q^{10} - 38q^{11} + 12q^{12} - q^{13} + 23q^{14} + 5q^{15} + 74q^{16} + 26q^{17} + 16q^{18} - 10q^{19} + 50q^{20} + 21q^{21} - 4q^{22} + 10q^{23} + 41q^{24} + 38q^{25} + 25q^{26} + 5q^{27} + 2q^{28} + 28q^{29} + 11q^{30} + 24q^{31} + 39q^{32} - 5q^{33} + 38q^{34} + 111q^{36} + 12q^{37} + 19q^{38} - 18q^{39} + 15q^{40} + 62q^{41} - 17q^{42} - 32q^{43} - 50q^{44} + 63q^{45} - 9q^{46} + 31q^{47} + 53q^{48} + 88q^{49} + 4q^{50} - 3q^{51} - 21q^{52} + 30q^{53} + 49q^{54} - 38q^{55} + 32q^{56} + 49q^{57} + 12q^{58} + 31q^{59} + 12q^{60} + 25q^{61} + 12q^{62} + 15q^{63} + 137q^{64} - q^{65} - 11q^{66} + 20q^{67} + 75q^{68} + 92q^{69} + 23q^{70} + 32q^{71} + 6q^{72} - 38q^{73} + 55q^{74} + 5q^{75} - 57q^{76} - 17q^{78} - 2q^{79} + 74q^{80} + 118q^{81} + 14q^{82} + 4q^{83} + 22q^{84} + 26q^{85} + 5q^{86} + 24q^{87} - 15q^{88} + 143q^{89} + 16q^{90} + 66q^{91} + 29q^{92} - 8q^{93} - 7q^{94} - 10q^{95} + 59q^{96} + 41q^{97} - 10q^{98} - 63q^{99} + O(q^{100}) \)

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 −2.76981 1.77605 5.67182 1.00000 −4.91932 −0.953960 −10.1702 0.154367 −2.76981
1.2 −2.64676 −3.26170 5.00536 1.00000 8.63297 0.334745 −7.95449 7.63872 −2.64676
1.3 −2.64612 −1.80895 5.00197 1.00000 4.78670 −4.64214 −7.94360 0.272285 −2.64612
1.4 −2.40266 2.98645 3.77280 1.00000 −7.17544 4.58733 −4.25943 5.91889 −2.40266
1.5 −2.35033 0.502249 3.52405 1.00000 −1.18045 0.984719 −3.58202 −2.74775 −2.35033
1.6 −2.26509 0.846807 3.13061 1.00000 −1.91809 −3.17432 −2.56093 −2.28292 −2.26509
1.7 −1.83787 −3.02191 1.37778 1.00000 5.55388 4.06050 1.14356 6.13192 −1.83787
1.8 −1.73652 −1.80706 1.01551 1.00000 3.13799 −4.26912 1.70959 0.265453 −1.73652
1.9 −1.69384 0.407884 0.869088 1.00000 −0.690890 2.45284 1.91558 −2.83363 −1.69384
1.10 −1.61749 2.78278 0.616262 1.00000 −4.50111 −5.17171 2.23818 4.74386 −1.61749
1.11 −1.50911 −0.619433 0.277405 1.00000 0.934791 1.62740 2.59958 −2.61630 −1.50911
1.12 −1.49358 2.85677 0.230796 1.00000 −4.26684 0.0973246 2.64246 5.16116 −1.49358
1.13 −1.16964 −3.05105 −0.631953 1.00000 3.56861 −2.34807 3.07843 6.30888 −1.16964
1.14 −1.00909 −1.30445 −0.981746 1.00000 1.31630 1.28192 3.00884 −1.29840 −1.00909
1.15 −0.454453 2.93224 −1.79347 1.00000 −1.33257 4.01407 1.72395 5.59806 −0.454453
1.16 −0.445505 −0.895604 −1.80153 1.00000 0.398996 −1.53298 1.69360 −2.19789 −0.445505
1.17 −0.364998 1.30973 −1.86678 1.00000 −0.478050 −1.97253 1.41137 −1.28460 −0.364998
1.18 −0.0798923 0.0600931 −1.99362 1.00000 −0.00480098 −4.79075 0.319059 −2.99639 −0.0798923
1.19 0.0204713 2.32254 −1.99958 1.00000 0.0475455 2.78561 −0.0818767 2.39419 0.0204713
1.20 0.0631532 0.00106429 −1.99601 1.00000 6.72133e−5 0 3.26238 −0.252361 −3.00000 0.0631532
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.38
Significant digits:
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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 4015.2.a.i 38
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4015.2.a.i 38 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(11\) \(1\)
\(73\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{38} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4015))\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database