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Properties

Label 441.4.bg
Level $441$
Weight $4$
Character orbit 441.bg
Rep. character $\chi_{441}(17,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $672$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

Total New Old
Modular forms 2064 672 1392
Cusp forms 1968 672 1296
Eisenstein series 96 0 96

Trace form

\( 672 q - 224 q^{4} - 56 q^{7} + O(q^{10}) \) \( 672 q - 224 q^{4} - 56 q^{7} + 72 q^{10} + 896 q^{16} + 612 q^{19} + 336 q^{22} + 1148 q^{25} - 1288 q^{28} - 1128 q^{31} + 1008 q^{34} + 1960 q^{37} - 1836 q^{40} - 952 q^{43} + 420 q^{46} + 4592 q^{49} + 6524 q^{52} + 1764 q^{55} - 2016 q^{58} + 596 q^{61} + 1624 q^{64} - 980 q^{67} - 5544 q^{70} - 4068 q^{73} - 4284 q^{76} + 2296 q^{79} - 1992 q^{82} - 4368 q^{85} - 2520 q^{88} - 8652 q^{91} - 276 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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