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Properties

Label 441.6.bg
Level $441$
Weight $6$
Character orbit 441.bg
Rep. character $\chi_{441}(17,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1128$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 3408 1128 2280
Cusp forms 3312 1128 2184
Eisenstein series 96 0 96

Trace form

\( 1128 q - 1536 q^{4} - 54 q^{7} + O(q^{10}) \) \( 1128 q - 1536 q^{4} - 54 q^{7} - 1488 q^{10} + 25600 q^{16} + 2202 q^{19} + 17176 q^{22} + 65342 q^{25} - 9464 q^{28} - 30798 q^{31} + 86128 q^{34} + 22580 q^{37} + 383476 q^{40} + 596 q^{43} + 14180 q^{46} - 179706 q^{49} + 146188 q^{52} + 82236 q^{55} + 344208 q^{58} + 232434 q^{61} + 1067160 q^{64} - 38810 q^{67} + 1347448 q^{70} + 518478 q^{73} + 58884 q^{76} - 205878 q^{79} - 199720 q^{82} - 174144 q^{85} + 50088 q^{88} + 512234 q^{91} + 1026668 q^{94} + O(q^{100}) \)

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

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