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Properties

Label 441.6.p
Level $441$
Weight $6$
Character orbit 441.p
Rep. character $\chi_{441}(80,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $132$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 592 132 460
Cusp forms 528 132 396
Eisenstein series 64 0 64

Trace form

\( 132 q + 1024 q^{4} + O(q^{10}) \) \( 132 q + 1024 q^{4} - 1488 q^{10} - 17032 q^{16} + 2202 q^{19} - 9000 q^{22} - 29554 q^{25} - 30798 q^{31} + 1998 q^{37} - 160284 q^{40} - 516 q^{43} - 14916 q^{46} + 98700 q^{52} - 276248 q^{58} + 11892 q^{61} - 358152 q^{64} - 7702 q^{67} + 518478 q^{73} - 136146 q^{79} - 1080180 q^{82} + 27920 q^{85} - 848240 q^{88} + 1716756 q^{94} + O(q^{100}) \)

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

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