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Properties

Label 441.4.bn
Level $441$
Weight $4$
Character orbit 441.bn
Rep. character $\chi_{441}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1992$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.bn (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 441 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

Total New Old
Modular forms 2040 2040 0
Cusp forms 1992 1992 0
Eisenstein series 48 48 0

Trace form

\( 1992 q - 21 q^{2} - 11 q^{3} + 1307 q^{4} - 18 q^{5} - 10 q^{6} - 12 q^{7} - 83 q^{9} + O(q^{10}) \) \( 1992 q - 21 q^{2} - 11 q^{3} + 1307 q^{4} - 18 q^{5} - 10 q^{6} - 12 q^{7} - 83 q^{9} - 22 q^{10} - 18 q^{11} + 570 q^{12} + 29 q^{13} - 600 q^{14} + 59 q^{15} - 5141 q^{16} + 72 q^{17} + 39 q^{18} - 36 q^{19} - 45 q^{20} + 67 q^{21} - 21 q^{22} + 108 q^{23} + 100 q^{24} + 3942 q^{25} + 96 q^{26} - 362 q^{27} + 128 q^{28} + 111 q^{29} + 14 q^{30} - 21 q^{32} - 11 q^{33} - 31 q^{34} - 765 q^{35} + 130 q^{36} + 1066 q^{37} + 684 q^{38} - 180 q^{39} - 427 q^{40} - 639 q^{41} + 1304 q^{42} - 89 q^{43} - 795 q^{44} - 3833 q^{45} + 3234 q^{46} - 1005 q^{47} + 1569 q^{48} + 72 q^{49} + 675 q^{50} - 95 q^{51} + 2492 q^{52} - 1092 q^{53} + 2371 q^{54} - 2170 q^{55} - 87 q^{56} + 1871 q^{57} + 3252 q^{58} - 1515 q^{59} + 1389 q^{60} + 2933 q^{61} + 3072 q^{62} + 622 q^{63} + 19548 q^{64} - 21 q^{65} - 5676 q^{66} + 576 q^{67} - 3525 q^{68} - 4469 q^{69} + 98 q^{70} - 9702 q^{71} - 1698 q^{72} - 22 q^{73} + 1194 q^{74} - 6911 q^{75} - 759 q^{76} + 4422 q^{77} - 10119 q^{78} - 180 q^{79} + 4239 q^{80} - 8455 q^{81} - 46 q^{82} - 1851 q^{83} + 8567 q^{84} - 130 q^{85} + 4140 q^{86} - 2755 q^{87} + 616 q^{88} + 10014 q^{89} + 11140 q^{90} + 1112 q^{91} - 6045 q^{92} - 11279 q^{93} - 7 q^{94} - 21 q^{95} + 1450 q^{96} + 792 q^{97} - 5667 q^{98} + 9845 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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