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Properties

Label 361.6.e
Level $361$
Weight $6$
Character orbit 361.e
Rep. character $\chi_{361}(28,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $804$
Sturm bound $190$

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Defining parameters

Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 361.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(190\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(361, [\chi])\).

Total New Old
Modular forms 1008 900 108
Cusp forms 888 804 84
Eisenstein series 120 96 24

Trace form

\( 804 q + 6 q^{2} + 39 q^{3} - 24 q^{4} + 6 q^{5} + 264 q^{6} + 357 q^{7} - 573 q^{8} + 105 q^{9} + O(q^{10}) \) \( 804 q + 6 q^{2} + 39 q^{3} - 24 q^{4} + 6 q^{5} + 264 q^{6} + 357 q^{7} - 573 q^{8} + 105 q^{9} + 957 q^{10} + 477 q^{11} - 861 q^{12} - 2391 q^{13} - 669 q^{14} - 3543 q^{15} + 3867 q^{17} + 12660 q^{18} - 1878 q^{20} + 2058 q^{21} - 5034 q^{22} + 1722 q^{23} - 6096 q^{24} - 4140 q^{25} - 3957 q^{26} - 858 q^{27} + 23280 q^{28} - 4563 q^{29} + 11514 q^{30} - 23841 q^{31} - 18219 q^{32} - 10965 q^{33} - 24912 q^{34} + 21570 q^{35} + 64785 q^{36} + 20064 q^{37} + 43152 q^{39} + 69882 q^{40} + 8415 q^{41} - 105357 q^{42} + 18195 q^{43} - 29841 q^{44} - 69090 q^{45} - 83112 q^{46} - 40761 q^{47} - 168777 q^{48} - 602577 q^{49} - 39594 q^{50} + 20385 q^{51} + 88755 q^{52} - 28239 q^{53} + 313761 q^{54} + 29322 q^{55} + 99618 q^{56} - 101016 q^{58} + 188352 q^{59} + 124164 q^{60} + 92676 q^{61} + 49884 q^{62} - 322200 q^{63} - 1240521 q^{64} - 271482 q^{65} - 378912 q^{66} - 418206 q^{67} - 225432 q^{68} - 162690 q^{69} + 86157 q^{70} + 313254 q^{71} + 70230 q^{72} + 561492 q^{73} - 137451 q^{74} + 44658 q^{75} + 671292 q^{77} + 1055091 q^{78} + 93891 q^{79} - 150621 q^{80} + 53382 q^{81} - 742539 q^{82} - 458640 q^{83} - 892659 q^{84} - 660468 q^{85} - 844344 q^{86} - 144249 q^{87} - 549381 q^{88} - 147528 q^{89} + 747942 q^{90} - 342399 q^{91} + 1597476 q^{92} + 599751 q^{93} + 1213398 q^{94} + 855258 q^{96} + 594912 q^{97} - 186957 q^{98} - 682629 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(361, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(361, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(361, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)