Properties

Label 2736.3.z
Level $2736$
Weight $3$
Character orbit 2736.z
Rep. character $\chi_{2736}(683,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $640$
Sturm bound $1440$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.z (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
Character field: \(\Q(i)\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 1936 640 1296
Cusp forms 1904 640 1264
Eisenstein series 32 0 32

Trace form

\( 640q + O(q^{10}) \) \( 640q + 112q^{16} + 64q^{19} + 4480q^{49} - 128q^{61} - 96q^{64} + 336q^{76} - 400q^{82} - 640q^{85} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)