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Properties

Label 1216.3.bh
Level $1216$
Weight $3$
Character orbit 1216.bh
Rep. character $\chi_{1216}(129,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $468$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.bh (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 1992 492 1500
Cusp forms 1848 468 1380
Eisenstein series 144 24 120

Trace form

\( 468 q + 12 q^{5} - 12 q^{9} + O(q^{10}) \) \( 468 q + 12 q^{5} - 12 q^{9} - 36 q^{13} - 12 q^{17} + 102 q^{21} - 12 q^{25} + 12 q^{29} + 42 q^{33} + 132 q^{41} + 6 q^{45} - 1392 q^{49} + 12 q^{53} - 12 q^{57} + 684 q^{61} - 18 q^{65} - 846 q^{69} - 12 q^{73} - 852 q^{77} + 270 q^{81} + 972 q^{85} - 12 q^{89} - 798 q^{93} - 12 q^{97} + O(q^{100}) \)

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

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