Properties

Label 441.4.s
Level $441$
Weight $4$
Character orbit 441.s
Rep. character $\chi_{441}(362,\cdot)$
Character field $\Q(\zeta_{6})$
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.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 232q + 3q^{2} + 3q^{3} + 447q^{4} + 6q^{5} + 24q^{6} + 19q^{9} + O(q^{10}) \) \( 232q + 3q^{2} + 3q^{3} + 447q^{4} + 6q^{5} + 24q^{6} + 19q^{9} + 6q^{10} + 3q^{12} - 36q^{13} + 197q^{15} - 1657q^{16} - 72q^{17} - 49q^{18} + 6q^{19} + 24q^{20} - 20q^{22} + 66q^{24} + 5002q^{25} - 96q^{26} + 432q^{27} + 114q^{29} - 1866q^{30} - 177q^{31} + 1191q^{32} - 849q^{33} + 24q^{34} - 1280q^{36} - 82q^{37} + 1746q^{38} + 745q^{39} + 618q^{41} - 88q^{43} + 1563q^{44} - 303q^{45} - 218q^{46} + 201q^{47} - 1569q^{48} + 2955q^{50} - 423q^{51} + 36q^{53} + 684q^{54} - 2074q^{57} + 538q^{58} - 747q^{59} - 534q^{60} + 1209q^{61} - 2904q^{62} - 11168q^{64} + 2835q^{65} - 1029q^{66} - 295q^{67} - 7008q^{68} - 1005q^{69} + 3371q^{72} + 6q^{73} + 1788q^{75} - 144q^{76} + 8027q^{78} + 1019q^{79} - 4239q^{80} - 4809q^{81} - 18q^{82} + 1830q^{83} + 591q^{85} + 2130q^{87} - 1342q^{88} + 4266q^{89} + 9993q^{90} - 9786q^{92} + 613q^{93} + 3q^{94} + 867q^{95} - 5034q^{96} - 792q^{97} - 2259q^{99} + O(q^{100}) \)

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

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