Properties

Label 1764.3.s
Level $1764$
Weight $3$
Character orbit 1764.s
Rep. character $\chi_{1764}(587,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $944$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1764.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1764, [\chi])\).

Total New Old
Modular forms 1376 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944 q + 6 q^{2} + 2 q^{4} + 8 q^{9} + O(q^{10}) \) \( 944 q + 6 q^{2} + 2 q^{4} + 8 q^{9} + 2 q^{16} - 62 q^{18} - 20 q^{22} - 2196 q^{25} - 168 q^{29} - 106 q^{30} - 174 q^{32} - 180 q^{36} + 16 q^{37} + 40 q^{46} - 162 q^{50} + 88 q^{57} + 18 q^{58} + 734 q^{60} - 16 q^{64} - 276 q^{65} + 306 q^{72} - 294 q^{74} + 166 q^{78} - 392 q^{81} + 92 q^{85} + 582 q^{86} + 130 q^{88} - 912 q^{92} + 240 q^{93} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1764, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1764, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)