↑

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 $224$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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