Properties

Label 6025.2.a.q
Level $6025$
Weight $2$
Character orbit 6025.a
Self dual yes
Analytic conductor $48.110$
Analytic rank $0$
Dimension $66$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(66\)
Twist minimal: no (minimal twist has level 1205)
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.

\(\operatorname{Tr}(f)(q) = \) \( 66q + 78q^{4} + 16q^{6} + 90q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 66q + 78q^{4} + 16q^{6} + 90q^{9} + 48q^{11} + 30q^{14} + 98q^{16} + 12q^{19} + 18q^{21} + 42q^{24} + 48q^{26} + 56q^{29} + 48q^{31} + 8q^{34} + 158q^{36} + 84q^{39} + 56q^{41} + 144q^{44} + 36q^{46} + 98q^{49} + 44q^{51} + 86q^{54} + 104q^{56} + 108q^{59} + 22q^{61} + 136q^{64} + 74q^{66} + 20q^{69} + 212q^{71} + 84q^{74} + 6q^{76} + 66q^{79} + 162q^{81} - 52q^{84} + 100q^{86} + 54q^{89} + 72q^{91} - 96q^{94} + 122q^{96} + 112q^{99} + O(q^{100}) \)

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 −2.81437 0.650611 5.92068 0 −1.83106 −2.61686 −11.0342 −2.57671 0
1.2 −2.73687 −1.37229 5.49044 0 3.75578 −0.639768 −9.55288 −1.11681 0
1.3 −2.70326 −3.35528 5.30763 0 9.07021 3.43095 −8.94141 8.25791 0
1.4 −2.60935 2.94245 4.80870 0 −7.67788 2.28979 −7.32887 5.65803 0
1.5 −2.55975 2.19931 4.55230 0 −5.62967 −4.06530 −6.53325 1.83695 0
1.6 −2.48606 −2.54168 4.18051 0 6.31876 −3.51286 −5.42088 3.46011 0
1.7 −2.48219 −1.89252 4.16124 0 4.69758 −3.72710 −5.36461 0.581628 0
1.8 −2.37391 0.703313 3.63543 0 −1.66960 4.47866 −3.88235 −2.50535 0
1.9 −2.33352 1.59052 3.44531 0 −3.71151 −3.91727 −3.37267 −0.470249 0
1.10 −2.31942 −2.66924 3.37972 0 6.19110 0.0358936 −3.20016 4.12486 0
1.11 −2.20997 −2.26852 2.88397 0 5.01336 0.372373 −1.95355 2.14617 0
1.12 −2.06213 2.32228 2.25239 0 −4.78886 3.49367 −0.520471 2.39299 0
1.13 −1.90752 0.479938 1.63863 0 −0.915491 1.00580 0.689327 −2.76966 0
1.14 −1.85162 0.305536 1.42851 0 −0.565737 −2.51443 1.05818 −2.90665 0
1.15 −1.85071 2.57343 1.42511 0 −4.76266 −3.52351 1.06395 3.62254 0
1.16 −1.67685 3.17567 0.811815 0 −5.32511 0.164609 1.99240 7.08488 0
1.17 −1.64329 −3.10101 0.700400 0 5.09585 −0.459168 2.13562 6.61624 0
1.18 −1.54552 −0.0372080 0.388631 0 0.0575057 5.06287 2.49040 −2.99862 0
1.19 −1.47177 −1.07414 0.166115 0 1.58089 −3.64779 2.69906 −1.84623 0
1.20 −1.38861 −0.0366779 −0.0717484 0 0.0509315 3.69082 2.87686 −2.99865 0
See all 66 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.66
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(241\) \(1\)

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6025.2.a.q 66
5.b even 2 1 inner 6025.2.a.q 66
5.c odd 4 2 1205.2.b.d 66
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1205.2.b.d 66 5.c odd 4 2
6025.2.a.q 66 1.a even 1 1 trivial
6025.2.a.q 66 5.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6025))\):

\(35\!\cdots\!81\)\( T_{2}^{46} - \)\(18\!\cdots\!53\)\( T_{2}^{44} + \)\(80\!\cdots\!51\)\( T_{2}^{42} - \)\(29\!\cdots\!53\)\( T_{2}^{40} + \)\(95\!\cdots\!74\)\( T_{2}^{38} - \)\(25\!\cdots\!99\)\( T_{2}^{36} + \)\(59\!\cdots\!38\)\( T_{2}^{34} - \)\(11\!\cdots\!39\)\( T_{2}^{32} + \)\(19\!\cdots\!05\)\( T_{2}^{30} - \)\(26\!\cdots\!55\)\( T_{2}^{28} + \)\(30\!\cdots\!19\)\( T_{2}^{26} - \)\(29\!\cdots\!22\)\( T_{2}^{24} + \)\(23\!\cdots\!98\)\( T_{2}^{22} - \)\(14\!\cdots\!86\)\( T_{2}^{20} + \)\(73\!\cdots\!27\)\( T_{2}^{18} - \)\(28\!\cdots\!10\)\( T_{2}^{16} + \)\(85\!\cdots\!89\)\( T_{2}^{14} - \)\(18\!\cdots\!24\)\( T_{2}^{12} + \)\(30\!\cdots\!62\)\( T_{2}^{10} - \)\(33\!\cdots\!31\)\( T_{2}^{8} + 246600093167 T_{2}^{6} - 11048999599 T_{2}^{4} + 253747673 T_{2}^{2} - 1841449 \)">\(T_{2}^{66} - \cdots\)
\(88\!\cdots\!21\)\( T_{3}^{48} + \)\(71\!\cdots\!90\)\( T_{3}^{46} - \)\(49\!\cdots\!46\)\( T_{3}^{44} + \)\(28\!\cdots\!67\)\( T_{3}^{42} - \)\(13\!\cdots\!25\)\( T_{3}^{40} + \)\(56\!\cdots\!45\)\( T_{3}^{38} - \)\(19\!\cdots\!48\)\( T_{3}^{36} + \)\(57\!\cdots\!33\)\( T_{3}^{34} - \)\(14\!\cdots\!76\)\( T_{3}^{32} + \)\(28\!\cdots\!31\)\( T_{3}^{30} - \)\(48\!\cdots\!79\)\( T_{3}^{28} + \)\(67\!\cdots\!17\)\( T_{3}^{26} - \)\(75\!\cdots\!17\)\( T_{3}^{24} + \)\(68\!\cdots\!46\)\( T_{3}^{22} - \)\(48\!\cdots\!20\)\( T_{3}^{20} + \)\(26\!\cdots\!32\)\( T_{3}^{18} - \)\(10\!\cdots\!07\)\( T_{3}^{16} + \)\(32\!\cdots\!23\)\( T_{3}^{14} - \)\(66\!\cdots\!68\)\( T_{3}^{12} + \)\(89\!\cdots\!84\)\( T_{3}^{10} - \)\(69\!\cdots\!00\)\( T_{3}^{8} + \)\(25\!\cdots\!48\)\( T_{3}^{6} - 205383271424 T_{3}^{4} + 427458560 T_{3}^{2} - 262144 \)">\(T_{3}^{66} - \cdots\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database