Properties

Label 49.22.c
Level $49$
Weight $22$
Character orbit 49.c
Rep. character $\chi_{49}(18,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $136$
Sturm bound $102$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(102\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(49, [\chi])\).

Total New Old
Modular forms 204 144 60
Cusp forms 188 136 52
Eisenstein series 16 8 8

Trace form

\( 136 q - 573 q^{2} - 118097 q^{3} - 70810345 q^{4} - 19296893 q^{5} + 457302020 q^{6} + 1280412774 q^{8} - 218667013405 q^{9} + O(q^{10}) \) \( 136 q - 573 q^{2} - 118097 q^{3} - 70810345 q^{4} - 19296893 q^{5} + 457302020 q^{6} + 1280412774 q^{8} - 218667013405 q^{9} - 45908292458 q^{10} + 116094841045 q^{11} - 703726516612 q^{12} - 573150555348 q^{13} + 2880852458002 q^{15} - 62888578987685 q^{16} - 3631296873225 q^{17} + 32035715280937 q^{18} - 56849486179647 q^{19} + 211235752093016 q^{20} + 696271124695836 q^{22} + 159906108938871 q^{23} + 151975129265904 q^{24} - 5811119052144029 q^{25} + 1358522589413276 q^{26} + 2144448281577238 q^{27} - 15989169328136488 q^{29} + 5944484277239358 q^{30} - 2915918111714909 q^{31} - 8497750454589467 q^{32} - 14438281026776999 q^{33} + 79038877574366724 q^{34} + 289226695395829850 q^{36} + 70239327775907151 q^{37} - 69816975237291142 q^{38} - 223105560390102670 q^{39} - 327938659319189184 q^{40} + 485968527188727716 q^{41} - 120786450050234984 q^{43} + 819504456563159268 q^{44} + 37395922860484930 q^{45} - 1455493298272396210 q^{46} - 545845114015708227 q^{47} + 4323454314028504928 q^{48} - 1463760786075534878 q^{50} - 1168590189847114457 q^{51} + 2470837410767658632 q^{52} + 3073284490028750019 q^{53} - 355603765001582734 q^{54} + 4587818432221886582 q^{55} - 7741323642927907794 q^{57} - 332930357316357442 q^{58} - 7474478541444602961 q^{59} + 29178095550829202852 q^{60} + 2848450223489054583 q^{61} - 63246313374361735548 q^{62} + 158367521183028357338 q^{64} - 27003943934162856402 q^{65} + 34922560371104300090 q^{66} - 45821203126569899419 q^{67} + 60830600544042602196 q^{68} - 55070614676968282518 q^{69} + 21849754602160092880 q^{71} - 56754182965666706259 q^{72} + 22389609053337927163 q^{73} + 295470313135892390396 q^{74} - 84570010377850408348 q^{75} - 71802870184863662824 q^{76} + 338865402408674009064 q^{78} + 217718684540539025495 q^{79} - 226029126485786363824 q^{80} - 1150569709194316278040 q^{81} - 126519604886693145484 q^{82} + 1235016850633512172968 q^{83} - 433811807898865883990 q^{85} - 97860353488040513984 q^{86} - 367683551076552943442 q^{87} - 2242483408387636647912 q^{88} - 31327966399121384405 q^{89} + 1322424440541914944136 q^{90} - 5430844411737840523608 q^{92} + 998275554458240910079 q^{93} - 279079228503504697758 q^{94} - 578851801795517216711 q^{95} - 81057395943474767264 q^{96} - 234002595919330799036 q^{97} + 6758782982330798119028 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{22}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{22}^{\mathrm{old}}(49, [\chi]) \cong \) \(S_{22}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)