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Properties

Label 1764.3.cx
Level $1764$
Weight $3$
Character orbit 1764.cx
Rep. character $\chi_{1764}(143,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2688$
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.cx (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 8160 2688 5472
Cusp forms 7968 2688 5280
Eisenstein series 192 0 192

Trace form

\( 2688 q + O(q^{10}) \) \( 2688 q - 24 q^{22} + 1136 q^{25} + 392 q^{28} + 560 q^{34} - 640 q^{37} + 724 q^{40} + 100 q^{46} + 128 q^{49} + 396 q^{52} + 176 q^{58} + 784 q^{61} - 264 q^{64} - 808 q^{70} - 720 q^{73} + 420 q^{76} + 1112 q^{82} - 120 q^{88} - 228 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(1764, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)