Properties

Label 441.4.o
Level $441$
Weight $4$
Character orbit 441.o
Rep. character $\chi_{441}(146,\cdot)$
Character field $\Q(\zeta_{6})$
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.o (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

\( 232q + 6q^{2} + 450q^{4} - 32q^{9} + O(q^{10}) \) \( 232q + 6q^{2} + 450q^{4} - 32q^{9} + 30q^{11} - 10q^{15} - 1678q^{16} + 170q^{18} + 28q^{22} - 54q^{23} - 2498q^{25} - 264q^{29} + 894q^{30} - 1758q^{32} + 1660q^{36} - 328q^{37} + 838q^{39} + 164q^{43} - 1064q^{46} + 822q^{50} + 420q^{51} - 1228q^{57} + 538q^{58} - 4986q^{60} - 11504q^{64} - 6354q^{65} + 590q^{67} - 4726q^{72} + 7890q^{74} + 1430q^{78} + 770q^{79} + 4776q^{81} + 966q^{85} + 19062q^{86} - 1246q^{88} + 8304q^{92} + 4000q^{93} - 6150q^{95} + 1062q^{99} + O(q^{100}) \)

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

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