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

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

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

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