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Properties

Label 1216.4.y
Level $1216$
Weight $4$
Character orbit 1216.y
Rep. character $\chi_{1216}(321,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $708$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1216.y (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(640\)

Dimensions

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

Total New Old
Modular forms 2952 732 2220
Cusp forms 2808 708 2100
Eisenstein series 144 24 120

Trace form

\( 708 q + 12 q^{5} - 12 q^{9} + O(q^{10}) \) \( 708 q + 12 q^{5} - 12 q^{9} - 204 q^{13} - 12 q^{17} + 210 q^{21} - 12 q^{25} + 12 q^{29} + 150 q^{33} + 24 q^{37} + 108 q^{41} + 6 q^{45} - 15588 q^{49} + 12 q^{53} - 12 q^{57} - 6468 q^{61} - 6 q^{65} - 1578 q^{69} - 12 q^{73} + 6420 q^{77} - 2610 q^{81} + 1452 q^{85} - 12 q^{89} - 11238 q^{93} - 12 q^{97} + O(q^{100}) \)

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

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