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Properties

Label 197.14.h
Level $197$
Weight $14$
Character orbit 197.h
Rep. character $\chi_{197}(4,\cdot)$
Character field $\Q(\zeta_{98})$
Dimension $8988$
Sturm bound $231$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.h (of order \(98\) and degree \(42\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 197 \)
Character field: \(\Q(\zeta_{98})\)
Sturm bound: \(231\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(197, [\chi])\).

Total New Old
Modular forms 9072 9072 0
Cusp forms 8988 8988 0
Eisenstein series 84 84 0

Trace form

\( 8988 q - 42 q^{2} - 42 q^{3} + 58576 q^{4} - 42 q^{5} + 653149 q^{6} - 570416 q^{7} - 57386 q^{8} - 42 q^{9} + O(q^{10}) \) \( 8988 q - 42 q^{2} - 42 q^{3} + 58576 q^{4} - 42 q^{5} + 653149 q^{6} - 570416 q^{7} - 57386 q^{8} - 42 q^{9} - 17281292 q^{10} - 17362100 q^{11} + 57302 q^{12} - 42 q^{13} - 238473690 q^{15} + 616875112 q^{16} - 42 q^{17} + 11160219 q^{18} + 1317284633 q^{19} - 49 q^{20} - 42 q^{21} - 2087933694 q^{22} - 42 q^{23} + 7782670294 q^{24} - 42 q^{25} + 12266811606 q^{26} - 7001459640 q^{27} - 15469506451 q^{28} - 95854458371 q^{29} - 9325687063 q^{30} + 19448615354 q^{31} - 1408884778 q^{32} + 78255251599 q^{33} + 27256178390 q^{34} - 42 q^{35} - 3434193533407 q^{36} - 120201345803 q^{37} + 57302 q^{38} - 10674616743 q^{39} + 44860190746 q^{40} - 38525717468 q^{41} + 284075937012 q^{42} - 197072963836 q^{43} + 2158654164702 q^{44} - 249927658806 q^{45} - 67702289648 q^{46} - 209875554287 q^{47} - 273745920042 q^{48} - 1061161041066 q^{49} + 1372261194402 q^{50} - 525862742566 q^{51} + 1237574873857 q^{52} - 42 q^{53} + 1514659462617 q^{54} - 1451283773604 q^{55} - 1705274669651 q^{56} - 10965551967041 q^{57} - 10227970749738 q^{58} - 1486154291146 q^{59} + 3369053518614 q^{60} - 698602605134 q^{61} - 809372710468 q^{62} + 1952032412239 q^{63} + 6068712741406 q^{64} + 5322360361549 q^{65} - 1333786063827 q^{66} + 6515229693728 q^{67} - 49 q^{68} - 49 q^{69} + 51269531208 q^{70} - 15275293227173 q^{71} + 34500763951136 q^{72} + 1667595396712 q^{73} - 1448925520042 q^{74} - 6114276222691 q^{75} + 3069061645153 q^{76} - 49 q^{77} - 11094832710696 q^{78} + 20549979749082 q^{79} - 469762090 q^{80} - 6382833710414 q^{81} - 42 q^{82} - 10034280083331 q^{83} + 639974006735 q^{84} - 53752953460598 q^{85} + 69781580600739 q^{86} - 49 q^{87} - 55949994187381 q^{88} - 13437250770916 q^{89} - 102774639072840 q^{90} - 11300980303830 q^{91} - 5378885148714 q^{92} + 18115725136537 q^{93} + 85960476064428 q^{94} - 65009579021156 q^{95} - 92926104562445 q^{96} + 3151454559750 q^{97} + 43853474184380 q^{98} - 54472232989461 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

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