Properties

Label 441.4.g
Level $441$
Weight $4$
Character orbit 441.g
Rep. character $\chi_{441}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $232$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 352 248 104
Cusp forms 320 232 88
Eisenstein series 32 16 16

Trace form

\( 232q - q^{2} + q^{3} - 449q^{4} - 38q^{5} + 20q^{6} + 47q^{9} + O(q^{10}) \) \( 232q - q^{2} + q^{3} - 449q^{4} - 38q^{5} + 20q^{6} + 47q^{9} + 18q^{10} + 18q^{11} + 41q^{12} + 14q^{13} - 239q^{15} - 1673q^{16} + 162q^{17} - 125q^{18} - 58q^{19} + 362q^{20} + 12q^{22} - 290q^{23} - 414q^{24} + 5002q^{25} + 266q^{26} - 272q^{27} - 462q^{29} - 762q^{30} - 61q^{31} + 29q^{32} - 23q^{33} - 6q^{34} + 1160q^{36} + 86q^{37} - 1522q^{38} + 833q^{39} - 36q^{40} + 692q^{41} + 80q^{43} - 5q^{44} + 1483q^{45} + 222q^{46} + 1005q^{47} + 1013q^{48} - 489q^{50} + 2449q^{51} - 670q^{52} - 434q^{53} - 910q^{54} + 870q^{55} - 198q^{57} + 474q^{58} + 1665q^{59} - 898q^{60} - 439q^{61} - 1812q^{62} + 11392q^{64} + 585q^{65} - 3073q^{66} - 295q^{67} - 2748q^{68} - 1389q^{69} - 1668q^{71} - 477q^{72} + 338q^{73} + 4154q^{74} + 1064q^{75} - 1006q^{76} + 2109q^{78} - 601q^{79} + 4817q^{80} - 3169q^{81} - 6q^{82} + 1356q^{83} - 849q^{85} - 8666q^{86} - 2774q^{87} + 834q^{88} + 2200q^{89} - 2665q^{90} + 1322q^{92} - 6443q^{93} + 1191q^{94} - 6353q^{95} + 1468q^{96} + 266q^{97} + 1967q^{99} + O(q^{100}) \)

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)