Properties

Label 441.4.h
Level $441$
Weight $4$
Character orbit 441.h
Rep. character $\chi_{441}(214,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $232$
Sturm bound $224$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.h (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

\( 232q + 2q^{2} + q^{3} + 898q^{4} + 19q^{5} + 20q^{6} + 5q^{9} + O(q^{10}) \) \( 232q + 2q^{2} + q^{3} + 898q^{4} + 19q^{5} + 20q^{6} + 5q^{9} + 18q^{10} - 9q^{11} + 62q^{12} + 14q^{13} - 239q^{15} + 3346q^{16} + 162q^{17} + 100q^{18} - 58q^{19} + 362q^{20} + 12q^{22} + 145q^{23} - 30q^{24} - 2501q^{25} + 266q^{26} - 272q^{27} - 462q^{29} + 231q^{30} + 122q^{31} - 58q^{32} - 77q^{33} - 6q^{34} + 1160q^{36} + 86q^{37} + 761q^{38} + 764q^{39} + 18q^{40} + 692q^{41} + 80q^{43} - 5q^{44} - 527q^{45} + 222q^{46} - 2010q^{47} + 1013q^{48} - 489q^{50} - 1475q^{51} + 335q^{52} - 434q^{53} - 577q^{54} + 870q^{55} - 198q^{57} - 237q^{58} - 3330q^{59} - 3001q^{60} + 878q^{61} - 1812q^{62} + 11392q^{64} - 1170q^{65} - 1330q^{66} + 590q^{67} + 1374q^{68} - 1389q^{69} - 1668q^{71} + 8232q^{72} + 338q^{73} - 2077q^{74} - 2737q^{75} - 1006q^{76} + 2109q^{78} + 1202q^{79} + 4817q^{80} + 701q^{81} - 6q^{82} + 1356q^{83} - 849q^{85} + 4333q^{86} + 5755q^{87} - 417q^{88} + 2200q^{89} - 2665q^{90} + 1322q^{92} + 469q^{93} - 2382q^{94} + 12706q^{95} + 5941q^{96} + 266q^{97} + 1967q^{99} + O(q^{100}) \)

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

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