Properties

Label 1216.4.t
Level $1216$
Weight $4$
Character orbit 1216.t
Rep. character $\chi_{1216}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $640$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1216, [\chi])\).

Total New Old
Modular forms 984 240 744
Cusp forms 936 240 696
Eisenstein series 48 0 48

Trace form

\( 240q + 1080q^{9} + O(q^{10}) \) \( 240q + 1080q^{9} + 3000q^{25} + 1392q^{33} + 120q^{41} + 10320q^{49} + 1368q^{57} + 432q^{73} - 6960q^{81} + 3168q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)