Properties

Label 441.4.i
Level $441$
Weight $4$
Character orbit 441.i
Rep. character $\chi_{441}(68,\cdot)$
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.i (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

\( 232q + 3q^{3} - 894q^{4} + 3q^{5} - 24q^{6} + 61q^{9} + O(q^{10}) \) \( 232q + 3q^{3} - 894q^{4} + 3q^{5} - 24q^{6} + 61q^{9} + 6q^{10} - 21q^{11} - 186q^{12} + 36q^{13} + 197q^{15} + 3314q^{16} + 72q^{17} + 158q^{18} + 6q^{19} - 24q^{20} - 20q^{22} + 441q^{23} + 114q^{24} - 2501q^{25} + 96q^{26} - 432q^{27} + 114q^{29} + 711q^{30} + 3q^{33} - 24q^{34} - 1280q^{36} - 82q^{37} + 873q^{38} - 446q^{39} - 420q^{40} - 618q^{41} - 88q^{43} - 1563q^{44} - 291q^{45} - 218q^{46} + 402q^{47} + 1569q^{48} + 2955q^{50} - 663q^{51} - 189q^{52} - 36q^{53} + 2385q^{54} - 2074q^{57} - 269q^{58} - 1494q^{59} - 1545q^{60} + 2904q^{62} - 11168q^{64} + 372q^{66} + 590q^{67} - 3504q^{68} + 1005q^{69} - 3640q^{72} + 6q^{73} - 4101q^{74} + 33q^{75} + 144q^{76} + 8027q^{78} - 2038q^{79} + 4239q^{80} + 4029q^{81} - 18q^{82} - 1830q^{83} + 591q^{85} - 6579q^{86} - 2013q^{87} + 671q^{88} - 4266q^{89} - 9993q^{90} - 9786q^{92} + 1861q^{93} - 3975q^{96} + 792q^{97} - 2259q^{99} + O(q^{100}) \)

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

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