Properties

Label 1849.4.a.i
Level $1849$
Weight $4$
Character orbit 1849.a
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $50$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(50\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 50q - 10q^{2} - 2q^{3} + 186q^{4} + 8q^{5} - 51q^{6} - 6q^{7} - 138q^{8} + 360q^{9} - 137q^{10} - 252q^{11} - 48q^{12} - 192q^{13} - 272q^{14} - 314q^{15} + 542q^{16} - 236q^{17} - 386q^{18} + 12q^{19} + 108q^{20} - 408q^{21} + 1235q^{22} - 630q^{23} - 613q^{24} + 1098q^{25} + 1493q^{26} + 10q^{27} - 242q^{28} + 208q^{29} - 48q^{30} - 932q^{31} - 1124q^{32} + 254q^{33} + 765q^{34} - 1452q^{35} + 747q^{36} - 90q^{37} - 1213q^{38} - 1610q^{39} - 1693q^{40} - 1354q^{41} - 16q^{42} - 2704q^{44} + 4508q^{45} + 233q^{46} - 3484q^{47} - 376q^{48} + 1324q^{49} - 408q^{50} + 4054q^{51} - 2176q^{52} - 726q^{53} - 6497q^{54} - 3288q^{55} - 7097q^{56} - 870q^{57} + 275q^{58} - 4370q^{59} - 3891q^{60} + 1172q^{61} - 1546q^{62} - 3686q^{63} + 606q^{64} + 2610q^{65} - 4697q^{66} - 344q^{67} - 3221q^{68} + 136q^{69} - 1310q^{70} + 162q^{71} - 5814q^{72} + 746q^{73} - 4332q^{74} + 236q^{75} + 1338q^{76} + 2024q^{77} - 2782q^{78} - 2656q^{79} - 5713q^{80} - 86q^{81} - 4168q^{82} - 3514q^{83} - 4269q^{84} - 7558q^{85} - 10278q^{87} + 11692q^{88} + 2640q^{89} - 8286q^{90} - 5946q^{91} - 4271q^{92} - 2q^{93} + 9062q^{94} - 12140q^{95} - 700q^{96} - 3864q^{97} - 2826q^{98} - 8174q^{99} + O(q^{100}) \)

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 −5.46223 9.09504 21.8360 −6.15202 −49.6792 2.59059 −75.5754 55.7197 33.6038
1.2 −5.40604 −2.51556 21.2252 −3.24888 13.5992 35.6131 −71.4960 −20.6720 17.5635
1.3 −5.33984 −6.59560 20.5139 12.0752 35.2195 18.2315 −66.8223 16.5020 −64.4799
1.4 −5.05256 9.36203 17.5283 14.1438 −47.3022 −13.7151 −48.1425 60.6475 −71.4625
1.5 −4.85844 −5.73018 15.6044 14.4569 27.8397 −13.1859 −36.9457 5.83494 −70.2380
1.6 −4.80125 −5.52870 15.0520 18.8098 26.5447 0.563586 −33.8585 3.56656 −90.3106
1.7 −4.78088 1.15757 14.8568 −21.3015 −5.53419 24.0536 −32.7814 −25.6600 101.840
1.8 −4.52050 −1.75128 12.4349 −13.0472 7.91667 4.32755 −20.0482 −23.9330 58.9799
1.9 −3.90499 3.52020 7.24897 −10.7056 −13.7464 28.1424 2.93275 −14.6082 41.8054
1.10 −3.81936 8.34786 6.58755 2.56409 −31.8835 −3.42361 5.39467 42.6867 −9.79321
1.11 −3.53489 7.81725 4.49548 1.07981 −27.6332 −33.3014 12.3881 34.1094 −3.81700
1.12 −3.52844 −3.06369 4.44988 −14.8551 10.8100 −18.1642 12.5264 −17.6138 52.4155
1.13 −3.43471 −1.13642 3.79726 −2.82850 3.90328 −33.5669 14.4352 −25.7086 9.71508
1.14 −3.22072 −8.71909 2.37305 13.5152 28.0818 −24.0687 18.1228 49.0226 −43.5288
1.15 −3.06679 −2.01332 1.40518 −11.9365 6.17442 −10.6583 20.2249 −22.9465 36.6067
1.16 −3.04766 −1.42990 1.28824 10.9474 4.35784 8.62569 20.4552 −24.9554 −33.3638
1.17 −2.53235 8.01322 −1.58719 20.7136 −20.2923 3.06093 24.2781 37.2117 −52.4541
1.18 −2.25115 4.02813 −2.93234 4.98765 −9.06790 5.25109 24.6103 −10.7742 −11.2279
1.19 −2.06784 −3.28982 −3.72402 0.905592 6.80284 0.553732 24.2434 −16.1771 −1.87262
1.20 −1.26350 −9.40007 −6.40356 −0.325119 11.8770 −8.80478 18.1989 61.3613 0.410789
See all 50 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.50
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(43\) \(-1\)

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 1849.4.a.i 50
43.b odd 2 1 1849.4.a.j yes 50
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.4.a.i 50 1.a even 1 1 trivial
1849.4.a.j yes 50 43.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(15\!\cdots\!82\)\( T_{2}^{37} - 153098536947 T_{2}^{36} - \)\(36\!\cdots\!46\)\( T_{2}^{35} - \)\(13\!\cdots\!65\)\( T_{2}^{34} + \)\(67\!\cdots\!06\)\( T_{2}^{33} + \)\(46\!\cdots\!17\)\( T_{2}^{32} - \)\(10\!\cdots\!63\)\( T_{2}^{31} - \)\(94\!\cdots\!79\)\( T_{2}^{30} + \)\(11\!\cdots\!60\)\( T_{2}^{29} + \)\(13\!\cdots\!37\)\( T_{2}^{28} - \)\(11\!\cdots\!44\)\( T_{2}^{27} - \)\(14\!\cdots\!34\)\( T_{2}^{26} + \)\(88\!\cdots\!16\)\( T_{2}^{25} + \)\(11\!\cdots\!01\)\( T_{2}^{24} - \)\(55\!\cdots\!27\)\( T_{2}^{23} - \)\(76\!\cdots\!44\)\( T_{2}^{22} + \)\(27\!\cdots\!74\)\( T_{2}^{21} + \)\(38\!\cdots\!51\)\( T_{2}^{20} - \)\(10\!\cdots\!46\)\( T_{2}^{19} - \)\(15\!\cdots\!42\)\( T_{2}^{18} + \)\(33\!\cdots\!08\)\( T_{2}^{17} + \)\(46\!\cdots\!86\)\( T_{2}^{16} - \)\(77\!\cdots\!77\)\( T_{2}^{15} - \)\(10\!\cdots\!20\)\( T_{2}^{14} + \)\(13\!\cdots\!64\)\( T_{2}^{13} + \)\(18\!\cdots\!08\)\( T_{2}^{12} - \)\(16\!\cdots\!32\)\( T_{2}^{11} - \)\(23\!\cdots\!88\)\( T_{2}^{10} + \)\(14\!\cdots\!80\)\( T_{2}^{9} + \)\(20\!\cdots\!08\)\( T_{2}^{8} - \)\(71\!\cdots\!88\)\( T_{2}^{7} - \)\(11\!\cdots\!52\)\( T_{2}^{6} + \)\(15\!\cdots\!00\)\( T_{2}^{5} + \)\(38\!\cdots\!20\)\( T_{2}^{4} + \)\(14\!\cdots\!04\)\( T_{2}^{3} - \)\(53\!\cdots\!20\)\( T_{2}^{2} - \)\(82\!\cdots\!40\)\( T_{2} + \)\(16\!\cdots\!28\)\( \)">\(T_{2}^{50} + \cdots\) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1849))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database