Properties

Label 441.6.bn
Level $441$
Weight $6$
Character orbit 441.bn
Rep. character $\chi_{441}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $3336$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.bn (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(441, [\chi])\).

Total New Old
Modular forms 3384 3384 0
Cusp forms 3336 3336 0
Eisenstein series 48 48 0

Trace form

\( 3336 q - 21 q^{2} - 11 q^{3} + 8827 q^{4} - 18 q^{5} + 170 q^{6} + 23 q^{7} + 937 q^{9} + O(q^{10}) \) \( 3336 q - 21 q^{2} - 11 q^{3} + 8827 q^{4} - 18 q^{5} + 170 q^{6} + 23 q^{7} + 937 q^{9} - 22 q^{10} - 18 q^{11} - 6102 q^{12} - 550 q^{13} - 8988 q^{14} - 310 q^{15} - 139333 q^{16} + 801 q^{17} + 879 q^{18} - 36 q^{19} - 117 q^{20} + 4105 q^{21} - 69 q^{22} + 81 q^{23} + 2332 q^{24} + 168742 q^{25} - 10128 q^{26} + 29707 q^{27} - 888 q^{28} - 17925 q^{29} - 298 q^{30} - 21 q^{32} - 11 q^{33} - 103 q^{34} - 3960 q^{35} - 21062 q^{36} + 33501 q^{37} - 15660 q^{38} + 10053 q^{39} - 9571 q^{40} - 28251 q^{41} - 86908 q^{42} + 9239 q^{43} + 33405 q^{44} + 190417 q^{45} - 123330 q^{46} - 141405 q^{47} - 48615 q^{48} - 7955 q^{49} + 47835 q^{50} + 23986 q^{51} - 121284 q^{52} - 7788 q^{53} - 176225 q^{54} + 99974 q^{55} - 104775 q^{56} - 1747 q^{57} - 65280 q^{58} + 59055 q^{59} + 40821 q^{60} - 173418 q^{61} - 78864 q^{62} + 95857 q^{63} + 2164652 q^{64} - 21 q^{65} + 868236 q^{66} - 1258 q^{67} - 191517 q^{68} + 328000 q^{69} + 127190 q^{70} - 487683 q^{71} - 129018 q^{72} - 22 q^{73} - 103818 q^{74} - 543122 q^{75} - 11463 q^{76} - 13875 q^{77} + 502617 q^{78} - 132058 q^{79} - 243225 q^{80} + 185669 q^{81} - 118 q^{82} + 246909 q^{83} - 445537 q^{84} - 3130 q^{85} - 278388 q^{86} + 272597 q^{87} + 34744 q^{88} - 154200 q^{89} + 1055224 q^{90} + 120083 q^{91} + 83883 q^{92} + 183169 q^{93} - 7 q^{94} - 21 q^{95} - 994190 q^{96} + 104037 q^{97} + 646797 q^{98} - 908044 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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