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Properties

Label 49.22
Level 49
Weight 22
Dimension 1951
Nonzero newspaces 4
Sturm bound 4312
Trace bound 1

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Defining parameters

Level: \( N \) = \( 49 = 7^{2} \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(4312\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(49))\).

Total New Old
Modular forms 2088 2000 88
Cusp forms 2028 1951 77
Eisenstein series 60 49 11

Trace form

\( 1951 q - 303 q^{2} - 365055 q^{3} - 2014223 q^{4} + 23047071 q^{5} + 762701175 q^{6} - 758495850 q^{7} - 5045643909 q^{8} - 45914200230 q^{9} + O(q^{10}) \) \( 1951 q - 303 q^{2} - 365055 q^{3} - 2014223 q^{4} + 23047071 q^{5} + 762701175 q^{6} - 758495850 q^{7} - 5045643909 q^{8} - 45914200230 q^{9} - 161657182545 q^{10} + 371608354605 q^{11} - 2598968961225 q^{12} - 557111614927 q^{13} - 1070170566990 q^{14} + 2103069012237 q^{15} - 2283100812023 q^{16} - 5348734563681 q^{17} + 127234801880517 q^{18} - 78946736880979 q^{19} + 917036982035307 q^{20} - 462555398005302 q^{21} + 423474781667793 q^{22} - 361160878055259 q^{23} + 123324672266343 q^{24} - 1700009249276348 q^{25} + 4088003739721251 q^{26} - 2706048339726825 q^{27} + 4390257669270438 q^{28} - 19052212953598773 q^{29} + 39908427775022271 q^{30} + 9848760162492281 q^{31} - 24996235060155123 q^{32} - 11928327873463059 q^{33} + 156221326628352879 q^{34} - 39845196618052854 q^{35} - 689328523991158425 q^{36} + 146968565288675723 q^{37} + 27090816682607547 q^{38} - 403018742384723451 q^{39} + 14830053787748043 q^{40} + 360438881299847553 q^{41} + 1179380453013586005 q^{42} - 537133365479463463 q^{43} - 1730197499245040541 q^{44} + 2716418244669839889 q^{45} + 1410220598452522479 q^{46} + 502028034668598681 q^{47} - 6245573765662564902 q^{48} + 16846790018756628 q^{49} - 1287947976924888150 q^{50} + 6687774171253809693 q^{51} - 17114397172562072845 q^{52} - 5238570254190615309 q^{53} + 18319375194155075847 q^{54} + 31197562850301544965 q^{55} - 40797118406549181348 q^{56} - 8525085636727691643 q^{57} + 25095418573444361607 q^{58} + 3848723201965352517 q^{59} - 33982030331656156365 q^{60} + 12480457033120534379 q^{61} - 40725446210082624741 q^{62} - 42328111320094070856 q^{63} - 31971712635932332649 q^{64} - 43676090431790245989 q^{65} - 155780521130700400737 q^{66} - 51335040854007605515 q^{67} + 172850346632272918791 q^{68} - 220176906808389938913 q^{69} + 98566573907133904593 q^{70} + 427426422109479201 q^{71} - 127302196629204692883 q^{72} + 123903470954789632535 q^{73} + 443907774334552047051 q^{74} - 171441462711439370517 q^{75} + 177034029107043696455 q^{76} - 53983804458236672880 q^{77} + 409620867975386859225 q^{78} + 392009900261934482813 q^{79} - 757171040469116802660 q^{80} + 29608312835951316552 q^{81} - 474044817995990912664 q^{82} + 129157134664949892711 q^{83} + 3541005761416036253046 q^{84} - 694280441839664171523 q^{85} - 3735367695813255046206 q^{86} - 2862865762951784999937 q^{87} + 648158114176533165852 q^{88} + 5134561837130606602083 q^{89} + 3310663006187271292218 q^{90} - 3657595356474321961293 q^{91} - 6073250659923735468270 q^{92} + 6767955802177368960465 q^{93} + 10049665684313959876104 q^{94} + 2554931697180747239337 q^{95} - 9127184561369372920926 q^{96} - 8132155294586110486720 q^{97} - 6752294253664568373996 q^{98} + 11085514816434471114432 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.22.a \(\chi_{49}(1, \cdot)\) 49.22.a.a 1 1
49.22.a.b 1
49.22.a.c 5
49.22.a.d 6
49.22.a.e 10
49.22.a.f 13
49.22.a.g 13
49.22.a.h 20
49.22.c \(\chi_{49}(18, \cdot)\) n/a 136 2
49.22.e \(\chi_{49}(8, \cdot)\) n/a 582 6
49.22.g \(\chi_{49}(2, \cdot)\) n/a 1164 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)