Properties

Label 3.26
Level 3
Weight 26
Dimension 5
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 17
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 26 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(17\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(3))\).

Total New Old
Modular forms 9 5 4
Cusp forms 7 5 2
Eisenstein series 2 0 2

Trace form

\( 5 q - 4002 q^{2} + 531441 q^{3} + 116355284 q^{4} + 407709006 q^{5} - 1782453114 q^{6} - 39309958472 q^{7} - 291312800760 q^{8} + 1412147682405 q^{9} + O(q^{10}) \) \( 5 q - 4002 q^{2} + 531441 q^{3} + 116355284 q^{4} + 407709006 q^{5} - 1782453114 q^{6} - 39309958472 q^{7} - 291312800760 q^{8} + 1412147682405 q^{9} + 6147590052564 q^{10} - 24134783749332 q^{11} + 34618009344372 q^{12} + 142994137728454 q^{13} + 281682671800272 q^{14} - 390085403083146 q^{15} - 378809104605424 q^{16} + 6183897836895738 q^{17} - 1130283004996962 q^{18} + 9614719536266548 q^{19} - 77002472769731976 q^{20} + 10663264277029944 q^{21} + 26761044671198856 q^{22} + 84783342948789624 q^{23} - 130050447316112376 q^{24} - 99189140617918789 q^{25} + 147840851396154660 q^{26} + 150094635296999121 q^{27} + 2191353545749530016 q^{28} - 2502539841117381594 q^{29} + 5622001512394220676 q^{30} + 954876643541101456 q^{31} - 21954104161995916512 q^{32} + 6505256343289039452 q^{33} - 1854027316439415972 q^{34} - 10429196484047083440 q^{35} + 32862168927235115604 q^{36} + 69152558317233520798 q^{37} - 318832149907630898760 q^{38} + 187748226389447040366 q^{39} + 524570550230746268208 q^{40} - 597401254139237025294 q^{41} + 652099689206655819984 q^{42} + 272662541690214829324 q^{43} - 1971518245902562385040 q^{44} + 115149065583709247886 q^{45} + 1122026015545224939216 q^{46} - 1317381085286900621232 q^{47} + 2746532159144226606096 q^{48} + 1759829504488690145757 q^{49} - 8748160206152998259166 q^{50} + 3772100494132165133010 q^{51} + 456938492077599979288 q^{52} + 562007823967323032094 q^{53} - 503417406786135051834 q^{54} + 9480212039078845571016 q^{55} + 17341408417833155830080 q^{56} - 9661681057738447542780 q^{57} - 31236506660525159082780 q^{58} + 32201402276983996948092 q^{59} - 49422263670781084662984 q^{60} - 35650844679114201340778 q^{61} + 75489372062508933475296 q^{62} - 11102293350334319017032 q^{63} - 27045286271674562960320 q^{64} + 77231798191654195817028 q^{65} - 85732038362088400645080 q^{66} - 83472346788757030801532 q^{67} + 303643995600011618215656 q^{68} - 103047076779758115574248 q^{69} - 183924416222173820086560 q^{70} + 383358431003395605774120 q^{71} - 82275339289628704525560 q^{72} + 73225288673685458167474 q^{73} - 525224845214049550608588 q^{74} + 355922403636181174181199 q^{75} + 235955349730005758966032 q^{76} - 1585949533175292431417184 q^{77} + 893336260671388338546132 q^{78} + 760218847521043733000320 q^{79} - 2337439770619285359693216 q^{80} + 398832215384362549316805 q^{81} + 3692827177594097874372396 q^{82} - 936536331267412457078796 q^{83} + 1404155691579558819001248 q^{84} - 3147845920523300761594308 q^{85} - 2134843460602993978402872 q^{86} + 1329414084492021374701230 q^{87} + 2854164686565702215990880 q^{88} - 1229086967010673719324222 q^{89} + 1736261009020856945587284 q^{90} + 6852388264039769311678736 q^{91} - 727913052083093798383392 q^{92} - 635639340921259388051088 q^{93} - 16997751485168022275936544 q^{94} + 2339560291274106904595064 q^{95} - 13229430648783271528771296 q^{96} - 17623548522544072790935382 q^{97} + 38198701780426394919644526 q^{98} - 6816375787393008053380692 q^{99} + O(q^{100}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
3.26.a \(\chi_{3}(1, \cdot)\) 3.26.a.a 2 1
3.26.a.b 3

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(3))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(3)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)