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Properties

Label 441.6.o
Level $441$
Weight $6$
Character orbit 441.o
Rep. character $\chi_{441}(146,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $392$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 576 408 168
Cusp forms 544 392 152
Eisenstein series 32 16 16

Trace form

\( 392 q + 6 q^{2} + 3074 q^{4} + 64 q^{9} + O(q^{10}) \) \( 392 q + 6 q^{2} + 3074 q^{4} + 64 q^{9} + 1146 q^{11} + 716 q^{15} - 47166 q^{16} - 2854 q^{18} + 124 q^{22} + 16020 q^{23} - 112498 q^{25} + 35808 q^{29} - 27354 q^{30} + 8322 q^{32} - 56372 q^{36} - 10308 q^{37} + 6790 q^{39} - 18492 q^{43} + 37672 q^{46} - 56490 q^{50} - 24516 q^{51} + 177854 q^{57} - 9902 q^{58} + 157782 q^{60} - 1380240 q^{64} - 132480 q^{65} - 1244 q^{67} + 244106 q^{72} - 506550 q^{74} + 365174 q^{78} - 204104 q^{79} + 357792 q^{81} - 11454 q^{85} - 529866 q^{86} - 69502 q^{88} + 591360 q^{92} + 167032 q^{93} + 1163562 q^{95} - 820320 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)