Properties

Label 7.22.c
Level $7$
Weight $22$
Character orbit 7.c
Rep. character $\chi_{7}(2,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $26$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 7.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(7, [\chi])\).

Total New Old
Modular forms 30 30 0
Cusp forms 26 26 0
Eisenstein series 4 4 0

Trace form

\( 26 q + 286 q^{2} + 118097 q^{3} - 11780748 q^{4} + 19296893 q^{5} - 457302020 q^{6} + 1244099388 q^{7} - 3356984640 q^{8} - 36260337262 q^{9} + O(q^{10}) \) \( 26 q + 286 q^{2} + 118097 q^{3} - 11780748 q^{4} + 19296893 q^{5} - 457302020 q^{6} + 1244099388 q^{7} - 3356984640 q^{8} - 36260337262 q^{9} + 45908292458 q^{10} - 96908527507 q^{11} + 703726516612 q^{12} + 573150555348 q^{13} - 519063760642 q^{14} - 1250393933326 q^{15} - 13121838202992 q^{16} + 3631296873225 q^{17} - 26768119563764 q^{18} + 56849486179647 q^{19} - 211235752093016 q^{20} + 287520772660135 q^{21} - 564206457341956 q^{22} - 56010101087361 q^{23} - 151975129265904 q^{24} - 672811740581052 q^{25} - 1358522589413276 q^{26} - 2144448281577238 q^{27} - 4826527281886156 q^{28} + 11056108922426564 q^{29} - 6230983254308858 q^{30} + 2915918111714909 q^{31} + 6031769195105696 q^{32} + 14438281026776999 q^{33} - 79038877574366724 q^{34} + 40323248296500001 q^{35} + 92042127456862576 q^{36} - 56690306381981455 q^{37} + 69816975237291142 q^{38} + 192986544424759946 q^{39} + 327938659319189184 q^{40} - 485968527188727716 q^{41} - 97625587586165296 q^{42} + 198454074593197048 q^{43} - 545860052256697724 q^{44} - 37395922860484930 q^{45} + 1062080303131000686 q^{46} + 545845114015708227 q^{47} - 4323454314028504928 q^{48} - 834179171614979974 q^{49} + 3759707778375489104 q^{50} + 220241766654585435 q^{51} - 2470837410767658632 q^{52} + 1066530642992301045 q^{53} + 355603765001582734 q^{54} - 4587818432221886582 q^{55} + 6023120323352639808 q^{56} - 2436016836137617690 q^{57} - 2647477665953695612 q^{58} + 7474478541444602961 q^{59} - 21033489989317069124 q^{60} - 2848450223489054583 q^{61} + 63246313374361735548 q^{62} - 2628048802502234510 q^{63} + 13199726305469796608 q^{64} + 14969380626438713594 q^{65} - 34922560371104300090 q^{66} + 6260905331410186617 q^{67} - 60830600544042602196 q^{68} + 55070614676968282518 q^{69} - 66171982028236816970 q^{70} - 19829692806806168640 q^{71} + 39591517263878049216 q^{72} - 22389609053337927163 q^{73} - 109307996679538553910 q^{74} + 84570010377850408348 q^{75} + 71802870184863662824 q^{76} - 67599586966274830733 q^{77} - 201547269737063893496 q^{78} - 152765407297011897977 q^{79} + 226029126485786363824 q^{80} + 284650712144159176523 q^{81} + 126519604886693145484 q^{82} - 1235016850633512172968 q^{83} + 262424412632001748940 q^{84} + 672057383707197482898 q^{85} + 385414116959388791048 q^{86} + 367683551076552943442 q^{87} + 575858305808050147728 q^{88} + 31327966399121384405 q^{89} - 1322424440541914944136 q^{90} + 318458511806028001240 q^{91} + 1274558836326262037544 q^{92} - 39704754034417637049 q^{93} + 279079228503504697758 q^{94} + 529353291415579422425 q^{95} + 81057395943474767264 q^{96} + 234002595919330799036 q^{97} - 5157755886664145781506 q^{98} - 237991978233977177452 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.22.c.a 7.c 7.c $26$ $19.563$ None \(286\) \(118097\) \(19296893\) \(1244099388\) $\mathrm{SU}(2)[C_{3}]$