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Properties

Label 1216.3.q
Level $1216$
Weight $3$
Character orbit 1216.q
Rep. character $\chi_{1216}(767,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $156$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1216, [\chi])\).

Total New Old
Modular forms 664 164 500
Cusp forms 616 156 460
Eisenstein series 48 8 40

Trace form

\( 156 q + 2 q^{5} + 220 q^{9} + O(q^{10}) \) \( 156 q + 2 q^{5} + 220 q^{9} + 18 q^{13} - 2 q^{17} - 64 q^{21} - 352 q^{25} + 2 q^{29} - 16 q^{33} - 152 q^{37} - 50 q^{41} - 56 q^{45} - 932 q^{49} + 2 q^{53} - 102 q^{57} - 46 q^{61} + 92 q^{65} + 428 q^{69} - 2 q^{73} - 288 q^{77} - 654 q^{81} - 114 q^{85} - 2 q^{89} + 128 q^{93} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)