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Properties

Label 1216.4.i
Level $1216$
Weight $4$
Character orbit 1216.i
Rep. character $\chi_{1216}(577,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $236$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 984 244 740
Cusp forms 936 236 700
Eisenstein series 48 8 40

Trace form

\( 236 q + 2 q^{5} - 1028 q^{9} + O(q^{10}) \) \( 236 q + 2 q^{5} - 1028 q^{9} + 74 q^{13} - 2 q^{17} - 64 q^{21} - 2752 q^{25} + 2 q^{29} + 408 q^{33} + 1016 q^{37} - 42 q^{41} - 600 q^{45} + 10380 q^{49} + 2 q^{53} - 294 q^{57} + 746 q^{61} + 492 q^{65} - 2212 q^{69} - 2 q^{73} + 6256 q^{77} - 7398 q^{81} - 1434 q^{85} - 2 q^{89} - 1792 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{4}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)