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Properties

Label 1764.4.bi
Level $1764$
Weight $4$
Character orbit 1764.bi
Rep. character $\chi_{1764}(391,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1424$
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.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
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 2048 1456 592
Cusp forms 1984 1424 560
Eisenstein series 64 32 32

Trace form

\( 1424 q + 2 q^{2} + 2 q^{4} - 16 q^{8} + 8 q^{9} + O(q^{10}) \) \( 1424 q + 2 q^{2} + 2 q^{4} - 16 q^{8} + 8 q^{9} + 2 q^{16} + 106 q^{18} + 28 q^{22} + 17004 q^{25} + 48 q^{29} - 526 q^{30} + 522 q^{32} + 1044 q^{36} + 16 q^{37} - 2044 q^{44} - 56 q^{46} + 954 q^{50} + 16 q^{53} + 1048 q^{57} - 30 q^{58} - 1882 q^{60} - 16 q^{64} + 540 q^{65} - 1062 q^{72} + 1398 q^{74} + 5482 q^{78} - 3680 q^{81} - 508 q^{85} + 42 q^{86} - 1022 q^{88} + 3528 q^{92} + 336 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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