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Properties

Label 441.6.e
Level $441$
Weight $6$
Character orbit 441.e
Rep. character $\chi_{441}(226,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $162$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(441, [\chi])\).

Total New Old
Modular forms 592 170 422
Cusp forms 528 162 366
Eisenstein series 64 8 56

Trace form

\( 162 q + q^{2} - 1225 q^{4} + 60 q^{5} + 54 q^{8} + O(q^{10}) \) \( 162 q + q^{2} - 1225 q^{4} + 60 q^{5} + 54 q^{8} - 282 q^{10} + 154 q^{11} + 236 q^{13} - 18493 q^{16} + 498 q^{17} - 3982 q^{19} - 1968 q^{20} + 9620 q^{22} - 9196 q^{23} - 47985 q^{25} + 15882 q^{26} - 12796 q^{29} - 16426 q^{31} - 6943 q^{32} + 41940 q^{34} - 11434 q^{37} + 27612 q^{38} - 50004 q^{40} - 43812 q^{41} + 6764 q^{43} - 62044 q^{44} - 15494 q^{46} + 40074 q^{47} - 37994 q^{50} - 27436 q^{52} + 76808 q^{53} - 41472 q^{55} + 50278 q^{58} - 1956 q^{59} - 13102 q^{61} - 282144 q^{62} + 389250 q^{64} - 132210 q^{65} - 111458 q^{67} + 61152 q^{68} + 525868 q^{71} + 37352 q^{73} + 216750 q^{74} + 586736 q^{76} - 7086 q^{79} + 28860 q^{80} - 2712 q^{82} - 639396 q^{83} - 259284 q^{85} + 137130 q^{86} - 338184 q^{88} + 189786 q^{89} + 1314448 q^{92} + 212502 q^{94} + 626250 q^{95} + 803528 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)