Properties

Label 1216.4.bl
Level $1216$
Weight $4$
Character orbit 1216.bl
Rep. character $\chi_{1216}(223,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $720$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.bl (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 2952 720 2232
Cusp forms 2808 720 2088
Eisenstein series 144 0 144

Trace form

\( 720q + O(q^{10}) \) \( 720q - 360q^{41} + 17640q^{49} + 1296q^{73} - 8280q^{81} + O(q^{100}) \)

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

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