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Properties

Label 1764.4.n
Level $1764$
Weight $4$
Character orbit 1764.n
Rep. character $\chi_{1764}(31,\cdot)$
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.n (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

\( 1424 q - q^{2} - q^{4} + 24 q^{6} - 16 q^{8} + 2 q^{9} + O(q^{10}) \) \( 1424 q - q^{2} - q^{4} + 24 q^{6} - 16 q^{8} + 2 q^{9} + 6 q^{10} + 3 q^{12} - q^{16} + 12 q^{17} + 103 q^{18} - 384 q^{20} - 20 q^{22} - 78 q^{24} - 33996 q^{25} + 30 q^{26} - 36 q^{29} + 1160 q^{30} - 951 q^{32} + 6 q^{33} - 24 q^{34} - 864 q^{36} + 4 q^{37} - 127 q^{44} + 666 q^{45} + 34 q^{46} + 81 q^{48} + 1377 q^{50} + 4 q^{53} - 498 q^{54} + 724 q^{57} - 30 q^{58} + 1886 q^{60} + 6 q^{61} - 16 q^{64} - 966 q^{65} - 645 q^{66} - 162 q^{69} + 3363 q^{72} + 12 q^{73} - 3966 q^{74} + 192 q^{76} - 1823 q^{78} + 4053 q^{80} + 1846 q^{81} + 30 q^{82} + 242 q^{85} - 8298 q^{86} - 1022 q^{88} - 3168 q^{89} + 3111 q^{90} - 846 q^{92} + 330 q^{93} + 3 q^{94} - 4842 q^{96} + O(q^{100}) \)

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

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