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Properties

Label 441.4.w
Level $441$
Weight $4$
Character orbit 441.w
Rep. character $\chi_{441}(62,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 1032 336 696
Cusp forms 984 336 648
Eisenstein series 48 0 48

Trace form

\( 336 q + 224 q^{4} + 44 q^{7} + O(q^{10}) \) \( 336 q + 224 q^{4} + 44 q^{7} - 896 q^{16} - 336 q^{22} - 1904 q^{25} - 728 q^{28} - 1008 q^{34} - 1204 q^{37} - 1008 q^{40} + 448 q^{43} + 840 q^{46} + 1720 q^{49} + 112 q^{52} - 1260 q^{55} - 504 q^{58} - 9548 q^{61} + 9128 q^{64} - 3472 q^{67} - 1620 q^{70} + 4284 q^{76} + 2072 q^{79} + 12180 q^{82} + 4368 q^{85} - 5040 q^{88} + 5952 q^{91} + 3192 q^{94} + O(q^{100}) \)

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

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