Properties

Label 1764.4.be
Level $1764$
Weight $4$
Character orbit 1764.be
Rep. character $\chi_{1764}(863,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $480$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1764.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1764, [\chi])\).

Total New Old
Modular forms 2080 480 1600
Cusp forms 1952 480 1472
Eisenstein series 128 0 128

Trace form

\( 480 q + O(q^{10}) \) \( 480 q + 144 q^{13} + 120 q^{16} - 456 q^{22} + 6168 q^{25} + 1008 q^{34} - 504 q^{37} - 492 q^{40} + 180 q^{46} + 708 q^{52} - 2856 q^{58} + 2160 q^{61} + 4248 q^{64} - 1320 q^{73} + 1368 q^{76} + 996 q^{82} - 5184 q^{85} + 1536 q^{88} + 3852 q^{94} + 2064 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)