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Properties

Label 5.34.a
Level $5$
Weight $34$
Character orbit 5.a
Rep. character $\chi_{5}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

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

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{34}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
5.34.a.a 5.a 1.a $5$ $34.491$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(30472\) \(-14988714\) \(-762939453125\) \(-65\!\cdots\!58\) $+$ $\mathrm{SU}(2)$ \(q+(6094-\beta _{1})q^{2}+(-2997861-296\beta _{1}+\cdots)q^{3}+\cdots\)
5.34.a.b 5.a 1.a $6$ $34.491$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(147350\) \(26513900\) \(915527343750\) \(19\!\cdots\!00\) $-$ $\mathrm{SU}(2)$ \(q+(24558+\beta _{1})q^{2}+(4418958+77\beta _{1}+\cdots)q^{3}+\cdots\)

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

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