Properties

Label 49.22.e
Level $49$
Weight $22$
Character orbit 49.e
Rep. character $\chi_{49}(8,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $582$
Sturm bound $102$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 49.e (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(102\)

Dimensions

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

Total New Old
Modular forms 594 594 0
Cusp forms 582 582 0
Eisenstein series 12 12 0

Trace form

\( 582 q - 5 q^{2} - 5 q^{3} - 100663301 q^{4} + 19999957 q^{5} + 674205691 q^{6} + 485603552 q^{7} - 5433556495 q^{8} - 287865665310 q^{9} + O(q^{10}) \) \( 582 q - 5 q^{2} - 5 q^{3} - 100663301 q^{4} + 19999957 q^{5} + 674205691 q^{6} + 485603552 q^{7} - 5433556495 q^{8} - 287865665310 q^{9} - 31804002011 q^{10} - 11962887151 q^{11} + 1453608782332 q^{12} + 334905642785 q^{13} + 6401838082157 q^{14} - 12012875343413 q^{15} - 105409489178877 q^{16} + 19845757214355 q^{17} + 43001085441904 q^{18} - 150333343303404 q^{19} + 262196704075873 q^{20} - 175034625345153 q^{21} + 177373156279071 q^{22} - 940404836848027 q^{23} - 2723193684896179 q^{24} - 9433005411903366 q^{25} - 2500291145711527 q^{26} - 1608839696504441 q^{27} + 8240145804807238 q^{28} - 14888919683861431 q^{29} + 13035152749114356 q^{30} - 27534360448387812 q^{31} + 32781689002490287 q^{32} + 2371747701896137 q^{33} + 40761686427467563 q^{34} + 48312996151103411 q^{35} - 213125774759105723 q^{36} + 19541297118141017 q^{37} + 121716404539933863 q^{38} - 72244126063961719 q^{39} - 428444798115449551 q^{40} - 193072032905394685 q^{41} + 486757897352605235 q^{42} - 69796531517373169 q^{43} - 491892456441181195 q^{44} - 1431302841318129363 q^{45} + 462984370824548773 q^{46} + 2859521564793335629 q^{47} + 529997469336663956 q^{48} - 506156298135984356 q^{49} - 439240395983852636 q^{50} + 2360347525283035533 q^{51} + 4639460602711055093 q^{52} - 3541294183064385165 q^{53} + 5574948780592960176 q^{54} + 19686053015792992257 q^{55} - 26932521415918373612 q^{56} + 14590931256510394464 q^{57} - 11119823011369260947 q^{58} + 1297950228514615461 q^{59} - 64222647185753806015 q^{60} + 1489786813793193403 q^{61} + 36302711513844372749 q^{62} - 24900431738684504226 q^{63} - 56094895797157606683 q^{64} - 13977119436649260563 q^{65} + 207378994335327183105 q^{66} - 33935981671982738640 q^{67} - 148900977773175101012 q^{68} + 110194736821392796277 q^{69} + 248120788494008485923 q^{70} + 174237940749781073489 q^{71} + 286946976730899072340 q^{72} + 138660248316481345183 q^{73} - 37180926034251107111 q^{74} + 175942612933119251817 q^{75} - 541490129433280965238 q^{76} - 278358716473000017603 q^{77} - 412077421210778676255 q^{78} + 144275032084210137644 q^{79} - 1375605918043034993880 q^{80} - 194539650519614522590 q^{81} + 474460963369926570016 q^{82} - 1066962859443779187001 q^{83} - 303689139405501197614 q^{84} + 1150585856871371536217 q^{85} - 2103720440683223214933 q^{86} + 156214130762738956415 q^{87} + 704391486355115709683 q^{88} + 850930666452432165675 q^{89} + 1798708883985099793290 q^{90} + 1283192936915676042431 q^{91} - 3826380735675547679008 q^{92} - 147725039556447379936 q^{93} + 4463968157904938265284 q^{94} + 908779309767987315154 q^{95} - 10133441393535537078078 q^{96} - 6107561493584604676756 q^{97} - 4457598610883458460399 q^{98} - 3976454918911050075344 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.