Properties

Label 49.22.g
Level $49$
Weight $22$
Character orbit 49.g
Rep. character $\chi_{49}(2,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1164$
Sturm bound $102$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 49.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(102\)

Dimensions

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

Total New Old
Modular forms 1188 1188 0
Cusp forms 1164 1164 0
Eisenstein series 24 24 0

Trace form

\( 1164 q - 13 q^{2} - 118111 q^{3} + 100663283 q^{4} - 19296907 q^{5} - 311408650 q^{6} - 1244099402 q^{7} + 5433556480 q^{8} + 261838353618 q^{9} + O(q^{10}) \) \( 1164 q - 13 q^{2} - 118111 q^{3} + 100663283 q^{4} - 19296907 q^{5} - 311408650 q^{6} - 1244099402 q^{7} + 5433556480 q^{8} + 261838353618 q^{9} - 45908292472 q^{10} + 245129529037 q^{11} - 2882852570731 q^{12} - 573150555362 q^{13} - 7472008649147 q^{14} + 12012875343398 q^{15} + 102326394926967 q^{16} - 24046265961207 q^{17} + 21500536429496 q^{18} + 114820369038774 q^{19} + 218116474250570 q^{20} - 287520772660149 q^{21} - 177373156279086 q^{22} + 796747116555559 q^{23} + 2861136286798300 q^{24} + 8587254007915494 q^{25} + 4532683477841806 q^{26} - 22483008328522 q^{27} - 3849888135536800 q^{28} + 14888919683861416 q^{29} + 6517544993497569 q^{30} + 31508469941478726 q^{31} - 43479052759024435 q^{32} - 14438281026777013 q^{33} + 37788505628629154 q^{34} - 88158192769156265 q^{35} - 795973954698275668 q^{36} + 18150059468551375 q^{37} - 227795433217289364 q^{38} - 27380996450778362 q^{39} + 627372293402455594 q^{40} + 76505918944183414 q^{41} + 692622555660980770 q^{42} - 45509545367137610 q^{43} - 2245853249940737486 q^{44} + 2680169354286261432 q^{45} + 2931970665554998472 q^{46} - 2723901025713588637 q^{47} - 8401857859246319804 q^{48} + 523003088154740984 q^{49} + 439240395983852600 q^{50} + 2536374767141644215 q^{51} - 24030408347346968966 q^{52} - 1946862668902743507 q^{53} + 15726366253560552009 q^{54} + 6354886575834895350 q^{55} - 13864596990630807736 q^{56} - 10393653307294935231 q^{57} + 41894109754060827692 q^{58} + 11233347387763078431 q^{59} - 14053709904394417586 q^{60} + 8703162235360482743 q^{61} - 35828086634946765194 q^{62} - 17427679581409566630 q^{63} - 255193910446691076852 q^{64} - 6988559718324630292 q^{65} - 283511772516890374716 q^{66} - 212196402744404154 q^{67} + 238400117437248294605 q^{68} - 225040460998302266912 q^{69} - 149554214586874581330 q^{70} - 174237940749781073504 q^{71} - 354233425613002505512 q^{72} - 55066133083535060179 q^{73} + 262330379108860202594 q^{74} - 262211346250307800836 q^{75} + 622030086354612052495 q^{76} + 224374912014763344723 q^{77} + 412209042914620943376 q^{78} + 77362387379231636032 q^{79} + 568706494069027550628 q^{80} + 877614071688443489665 q^{81} - 618394634943825856858 q^{82} + 189426143868581527726 q^{83} + 3844694900821537450660 q^{84} - 1150585856871371536232 q^{85} - 1247664325045304705649 q^{86} - 3775250764042816127930 q^{87} + 1397753450893945013737 q^{88} + 3376539767939374176021 q^{89} + 481910539686484966764 q^{90} - 4940788293389998003724 q^{91} + 4520476957386073605922 q^{92} + 5646694548492258849136 q^{93} + 5696621564259550911238 q^{94} + 3257118671108475686600 q^{95} - 345277007678405999070 q^{96} - 1459835015744663852924 q^{97} - 2294695642781109913597 q^{98} + 3976454918911050075308 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.