Properties

Label 5.34.a
Level 5
Weight 34
Character orbit a
Rep. character \(\chi_{5}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newforms 2
Sturm bound 17
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 34 \)
Character orbit: \([\chi]\) = 5.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(17\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{34}(\Gamma_0(5))\).

Total New Old
Modular forms 17 11 6
Cusp forms 15 11 4
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators.

\(5\)Dim.
\(+\)\(5\)
\(-\)\(6\)

Trace form

\(11q \) \(\mathstrut +\mathstrut 177822q^{2} \) \(\mathstrut +\mathstrut 11525186q^{3} \) \(\mathstrut +\mathstrut 30661957012q^{4} \) \(\mathstrut +\mathstrut 152587890625q^{5} \) \(\mathstrut +\mathstrut 19540822365112q^{6} \) \(\mathstrut -\mathstrut 46338728939658q^{7} \) \(\mathstrut +\mathstrut 3225430753821000q^{8} \) \(\mathstrut +\mathstrut 28143353573754403q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(11q \) \(\mathstrut +\mathstrut 177822q^{2} \) \(\mathstrut +\mathstrut 11525186q^{3} \) \(\mathstrut +\mathstrut 30661957012q^{4} \) \(\mathstrut +\mathstrut 152587890625q^{5} \) \(\mathstrut +\mathstrut 19540822365112q^{6} \) \(\mathstrut -\mathstrut 46338728939658q^{7} \) \(\mathstrut +\mathstrut 3225430753821000q^{8} \) \(\mathstrut +\mathstrut 28143353573754403q^{9} \) \(\mathstrut +\mathstrut 17834167480468750q^{10} \) \(\mathstrut -\mathstrut 137040905322086448q^{11} \) \(\mathstrut +\mathstrut 60971626392900112q^{12} \) \(\mathstrut +\mathstrut 994105514137102766q^{13} \) \(\mathstrut +\mathstrut 4590339907282590864q^{14} \) \(\mathstrut +\mathstrut 6332796325683593750q^{15} \) \(\mathstrut -\mathstrut 24668569537387288304q^{16} \) \(\mathstrut -\mathstrut 174344791525389819618q^{17} \) \(\mathstrut +\mathstrut 1211227884109649084006q^{18} \) \(\mathstrut +\mathstrut 2629949074795140559700q^{19} \) \(\mathstrut +\mathstrut 4330342756958007812500q^{20} \) \(\mathstrut -\mathstrut 21095513432538959561268q^{21} \) \(\mathstrut -\mathstrut 11286990651079412083096q^{22} \) \(\mathstrut +\mathstrut 62333637911030794355346q^{23} \) \(\mathstrut +\mathstrut 139941815401965803680800q^{24} \) \(\mathstrut +\mathstrut 256113708019256591796875q^{25} \) \(\mathstrut -\mathstrut 786731607430157962930428q^{26} \) \(\mathstrut +\mathstrut 338636629821008839676300q^{27} \) \(\mathstrut -\mathstrut 3115868286788324128981536q^{28} \) \(\mathstrut +\mathstrut 378346181417138086849650q^{29} \) \(\mathstrut -\mathstrut 962723368287353515625000q^{30} \) \(\mathstrut +\mathstrut 9489274917388754532551412q^{31} \) \(\mathstrut +\mathstrut 26005215441519452400962592q^{32} \) \(\mathstrut +\mathstrut 1642692718077028889156752q^{33} \) \(\mathstrut -\mathstrut 59758248825859006634077156q^{34} \) \(\mathstrut +\mathstrut 12903807775063781738281250q^{35} \) \(\mathstrut -\mathstrut 11659788249203695577395324q^{36} \) \(\mathstrut +\mathstrut 133921119169281602784846862q^{37} \) \(\mathstrut +\mathstrut 505006684026590239645411800q^{38} \) \(\mathstrut -\mathstrut 205827565276884828247277164q^{39} \) \(\mathstrut +\mathstrut 444673077049346923828125000q^{40} \) \(\mathstrut -\mathstrut 877611451105002939933434358q^{41} \) \(\mathstrut -\mathstrut 1167391858000793668973715936q^{42} \) \(\mathstrut -\mathstrut 92495886232735084451898694q^{43} \) \(\mathstrut +\mathstrut 5315865955569651150896348784q^{44} \) \(\mathstrut -\mathstrut 143302674417652435302734375q^{45} \) \(\mathstrut +\mathstrut 619109570141906666657909232q^{46} \) \(\mathstrut -\mathstrut 3894170809960417686673993698q^{47} \) \(\mathstrut +\mathstrut 17220199818666666799165381696q^{48} \) \(\mathstrut -\mathstrut 3030192770064635081806288073q^{49} \) \(\mathstrut +\mathstrut 4140241071581840515136718750q^{50} \) \(\mathstrut -\mathstrut 47573643586148402567779819628q^{51} \) \(\mathstrut -\mathstrut 41590127827476399212699255528q^{52} \) \(\mathstrut +\mathstrut 156563227269110886940338961686q^{53} \) \(\mathstrut -\mathstrut 118512469582114319958478211600q^{54} \) \(\mathstrut +\mathstrut 66919357060831730957031250000q^{55} \) \(\mathstrut -\mathstrut 247692830146152201826120593600q^{56} \) \(\mathstrut -\mathstrut 33607110592102782383869594600q^{57} \) \(\mathstrut -\mathstrut 231402277243182521036482067900q^{58} \) \(\mathstrut +\mathstrut 78861056269392051112575106500q^{59} \) \(\mathstrut +\mathstrut 133015676440418439941406250000q^{60} \) \(\mathstrut +\mathstrut 460572004107086189243411159102q^{61} \) \(\mathstrut +\mathstrut 536014589511457033791035265024q^{62} \) \(\mathstrut -\mathstrut 1563787994007206511931699103034q^{63} \) \(\mathstrut +\mathstrut 898600982945289990860257620032q^{64} \) \(\mathstrut -\mathstrut 579879270575365015563964843750q^{65} \) \(\mathstrut +\mathstrut 1733691229124148114347126597984q^{66} \) \(\mathstrut -\mathstrut 400301447551034298034555574418q^{67} \) \(\mathstrut +\mathstrut 5041910916091392617758749111144q^{68} \) \(\mathstrut -\mathstrut 2451289934963191952816775433884q^{69} \) \(\mathstrut -\mathstrut 2862939441720943264160156250000q^{70} \) \(\mathstrut +\mathstrut 2949132692311410957838822815132q^{71} \) \(\mathstrut -\mathstrut 7231385689119979182171909639000q^{72} \) \(\mathstrut -\mathstrut 15386476146017658598833492512554q^{73} \) \(\mathstrut +\mathstrut 16856105507994721092423523720404q^{74} \) \(\mathstrut +\mathstrut 268341647461056709289550781250q^{75} \) \(\mathstrut +\mathstrut 36596379905322155312335890643600q^{76} \) \(\mathstrut +\mathstrut 46058584922060308397847985058544q^{77} \) \(\mathstrut -\mathstrut 45152184871995014141159045031728q^{78} \) \(\mathstrut -\mathstrut 32310702355995093203016673933800q^{79} \) \(\mathstrut +\mathstrut 23451478507858982229003906250000q^{80} \) \(\mathstrut -\mathstrut 54580160052874719655322926405169q^{81} \) \(\mathstrut -\mathstrut 128752451332055475378604069526516q^{82} \) \(\mathstrut +\mathstrut 45475167144980311320038954371626q^{83} \) \(\mathstrut -\mathstrut 61546281392264432143537965085056q^{84} \) \(\mathstrut +\mathstrut 67612682666414411654357910156250q^{85} \) \(\mathstrut -\mathstrut 63337765913717881559650507641048q^{86} \) \(\mathstrut -\mathstrut 38030330953052174525222225679700q^{87} \) \(\mathstrut +\mathstrut 691679161832993789415604141212000q^{88} \) \(\mathstrut -\mathstrut 397344858730033166579522546806050q^{89} \) \(\mathstrut +\mathstrut 20685804123017397200622558593750q^{90} \) \(\mathstrut -\mathstrut 74303315401394981275600343251908q^{91} \) \(\mathstrut -\mathstrut 1116484363668251966439651529251168q^{92} \) \(\mathstrut -\mathstrut 483217130549593702040631640697688q^{93} \) \(\mathstrut +\mathstrut 1122704041630260318638566226897984q^{94} \) \(\mathstrut +\mathstrut 121035713257573343612670898437500q^{95} \) \(\mathstrut +\mathstrut 2807210387000286026593313187477632q^{96} \) \(\mathstrut +\mathstrut 1701361424317563414831140787172102q^{97} \) \(\mathstrut -\mathstrut 1984116428580865663437978238924146q^{98} \) \(\mathstrut -\mathstrut 129783286881254841865246015315504q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(5))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
5.34.a.a \(5\) \(34.491\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(30472\) \(-14988714\) \(-762939453125\) \(-6\!\cdots\!58\) \(+\) \(q+(6094-\beta _{1})q^{2}+(-2997861-296\beta _{1}+\cdots)q^{3}+\cdots\)
5.34.a.b \(6\) \(34.491\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(147350\) \(26513900\) \(915527343750\) \(19\!\cdots\!00\) \(-\) \(q+(24558+\beta _{1})q^{2}+(4418958+77\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{34}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces

\( S_{34}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{34}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)