Properties

Label 29.18.a.b
Level $29$
Weight $18$
Character orbit 29.a
Self dual yes
Analytic conductor $53.134$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 29 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 29.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.1344053299\)
Analytic rank: \(0\)
Dimension: \(21\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 21q + 256q^{2} + 23966q^{3} + 1452522q^{4} + 998272q^{5} + 3411526q^{6} + 2193368q^{7} - 138137226q^{8} + 1264832799q^{9} - 224469478q^{10} + 1203139534q^{11} - 5164251122q^{12} + 3854339312q^{13} + 25262272904q^{14} + 28324474306q^{15} + 196520815922q^{16} + 76444714794q^{17} + 75758949126q^{18} + 246497292428q^{19} - 46900976670q^{20} + 360937126704q^{21} - 275001533522q^{22} + 213498528140q^{23} - 451123453870q^{24} + 3898884886997q^{25} - 3609347694206q^{26} - 2718903745978q^{27} - 5946174617200q^{28} + 10505174672181q^{29} - 20237658929454q^{30} + 16670029895798q^{31} - 42141001912046q^{32} - 7157109761394q^{33} + 12785761151136q^{34} + 46677934312888q^{35} + 132137824374868q^{36} + 53445659988410q^{37} + 76581637956388q^{38} + 79233849032530q^{39} + 193617444734146q^{40} - 20814769309298q^{41} + 76690667258352q^{42} + 185498647364454q^{43} + 315429066899678q^{44} - 486270821438526q^{45} + 261474367677132q^{46} + 389503471719450q^{47} - 101509672247630q^{48} + 730079062141437q^{49} + 1482269666368354q^{50} + 718238208473988q^{51} + 1966802817157170q^{52} + 747441265526156q^{53} + 5692893333117030q^{54} + 1639109418219546q^{55} + 5657219329125240q^{56} + 4694352396864932q^{57} + 128063081718016q^{58} + 5280258638332960q^{59} + 15251367906033378q^{60} + 5813675353074254q^{61} + 6242066590947250q^{62} + 10947760075450368q^{63} + 24583792057508902q^{64} + 19190799243789974q^{65} + 41877805444482390q^{66} + 13420580230958268q^{67} + 24771837384165388q^{68} + 30973047049935252q^{69} + 8505088080182440q^{70} + 4824462822979508q^{71} + 1180071997284592q^{72} + 11228916281304662q^{73} - 89132715356772q^{74} + 59161419576630296q^{75} + 57466858643173460q^{76} + 58741564492720064q^{77} + 142050530910210210q^{78} + 71718598015696758q^{79} + 48350023652407550q^{80} + 75805931446703569q^{81} + 188661890754420812q^{82} + 50769377111735608q^{83} + 198832046985593048q^{84} + 53422044849490784q^{85} + 35014892323844118q^{86} + 11988905533023326q^{87} + 37459283979085258q^{88} - 70981414576978018q^{89} + 57211029866143724q^{90} + 112933943315157320q^{91} - 103019729095759724q^{92} - 350358290646906646q^{93} - 150286322409612578q^{94} - 102561321856584476q^{95} - 213770098354021866q^{96} - 130930167251505210q^{97} - 537387515497557296q^{98} - 95267700931431064q^{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 −716.767 6161.78 382683. −44516.1 −4.41656e6 −2.28029e7 −1.80347e8 −9.11726e7 3.19077e7
1.2 −687.348 −21372.9 341375. −1.16997e6 1.46906e7 −9.37855e6 −1.44551e8 3.27660e8 8.04176e8
1.3 −645.655 14883.2 285798. 954733. −9.60943e6 1.80737e7 −9.98999e7 9.23704e7 −6.16428e8
1.4 −553.336 −346.147 175108. 641880. 191536. −1.77073e7 −2.43669e7 −1.29020e8 −3.55175e8
1.5 −361.395 9478.77 −465.313 215546. −3.42559e6 −1.26142e7 4.75370e7 −3.92930e7 −7.78973e7
1.6 −332.840 −18225.8 −20289.6 −318485. 6.06628e6 9.82044e6 5.03792e7 2.03040e8 1.06005e8
1.7 −275.201 7065.32 −55336.6 −620891. −1.94438e6 2.72618e7 5.12998e7 −7.92215e7 1.70870e8
1.8 −237.844 −14184.6 −74502.2 1.22166e6 3.37373e6 1.05564e7 4.88946e7 7.20633e7 −2.90566e8
1.9 −65.9873 22515.6 −126718. 342266. −1.48575e6 1.63719e7 1.70108e7 3.77814e8 −2.25852e7
1.10 −39.6552 13037.0 −129499. −1.72282e6 −516984. −1.48112e7 1.03330e7 4.08230e7 6.83187e7
1.11 −3.42944 −6754.54 −131060. 511876. 23164.3 −1.86320e7 898966. −8.35164e7 −1.75545e6
1.12 59.1674 15524.2 −127571. 1.59085e6 918527. −2.66210e7 −1.53032e7 1.11861e8 9.41262e7
1.13 217.779 −424.636 −83644.2 −874312. −92476.9 3.28654e6 −4.67607e7 −1.28960e8 −1.90407e8
1.14 290.453 −16308.4 −46709.2 805745. −4.73681e6 2.28724e7 −5.16370e7 1.36823e8 2.34031e8
1.15 327.881 6727.77 −23565.9 1.45971e6 2.20591e6 2.18126e7 −5.07029e7 −8.38773e7 4.78610e8
1.16 361.094 −2259.76 −683.052 −433238. −815984. −1.41185e7 −4.75760e7 −1.24034e8 −1.56440e8
1.17 460.739 20203.5 81208.7 −1.66304e6 9.30854e6 1.23855e7 −2.29740e7 2.79040e8 −7.66230e8
1.18 500.684 −16927.2 119612. −1.40156e6 −8.47517e6 −1.54199e7 −5.73773e6 1.57390e8 −7.01740e8
1.19 616.905 17761.1 249500. 768235. 1.09569e7 1.64486e6 7.30585e7 1.86316e8 4.73928e8
1.20 652.859 4140.75 295153. 358296. 2.70332e6 1.05214e7 1.07122e8 −1.11994e8 2.33917e8
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(29\) \(-1\)

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 29.18.a.b 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
29.18.a.b 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(17\!\cdots\!68\)\( T_{2}^{17} - \)\(49\!\cdots\!40\)\( T_{2}^{16} - \)\(80\!\cdots\!52\)\( T_{2}^{15} + \)\(22\!\cdots\!96\)\( T_{2}^{14} + \)\(21\!\cdots\!08\)\( T_{2}^{13} - \)\(60\!\cdots\!92\)\( T_{2}^{12} - \)\(32\!\cdots\!04\)\( T_{2}^{11} + \)\(91\!\cdots\!24\)\( T_{2}^{10} + \)\(30\!\cdots\!32\)\( T_{2}^{9} - \)\(78\!\cdots\!36\)\( T_{2}^{8} - \)\(15\!\cdots\!40\)\( T_{2}^{7} + \)\(35\!\cdots\!44\)\( T_{2}^{6} + \)\(42\!\cdots\!40\)\( T_{2}^{5} - \)\(68\!\cdots\!92\)\( T_{2}^{4} - \)\(45\!\cdots\!52\)\( T_{2}^{3} + \)\(19\!\cdots\!68\)\( T_{2}^{2} + \)\(10\!\cdots\!40\)\( T_{2} + \)\(35\!\cdots\!00\)\( \)">\(T_{2}^{21} - \cdots\) acting on \(S_{18}^{\mathrm{new}}(\Gamma_0(29))\).