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Properties

Label 1764.3.bp
Level $1764$
Weight $3$
Character orbit 1764.bp
Rep. character $\chi_{1764}(251,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.bp (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 588 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1008\)

Dimensions

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

Total New Old
Modular forms 4080 1344 2736
Cusp forms 3984 1344 2640
Eisenstein series 96 0 96

Trace form

\( 1344 q + O(q^{10}) \) \( 1344 q + 24 q^{22} - 1088 q^{25} - 344 q^{28} - 560 q^{34} + 400 q^{37} - 784 q^{40} + 200 q^{46} - 128 q^{49} + 352 q^{58} - 784 q^{61} + 264 q^{64} + 1396 q^{70} - 420 q^{76} - 1820 q^{82} - 240 q^{88} - 1176 q^{94} + O(q^{100}) \)

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

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