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Properties

Label 1216.3.bv
Level $1216$
Weight $3$
Character orbit 1216.bv
Rep. character $\chi_{1216}(241,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $936$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1216.bv (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 3936 984 2952
Cusp forms 3744 936 2808
Eisenstein series 192 48 144

Trace form

\( 936 q + 12 q^{3} - 12 q^{5} + O(q^{10}) \) \( 936 q + 12 q^{3} - 12 q^{5} + 6 q^{11} - 12 q^{13} + 24 q^{15} - 24 q^{17} + 12 q^{19} - 66 q^{21} + 18 q^{27} - 12 q^{29} + 36 q^{31} - 24 q^{33} + 162 q^{35} + 12 q^{43} - 6 q^{45} + 24 q^{47} + 2760 q^{49} + 300 q^{51} - 12 q^{53} + 12 q^{59} - 12 q^{61} + 612 q^{63} - 36 q^{65} + 12 q^{67} + 846 q^{69} - 612 q^{77} + 24 q^{79} - 24 q^{81} + 6 q^{83} + 948 q^{85} + 306 q^{91} - 66 q^{93} + 24 q^{95} - 24 q^{97} + 498 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1216, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)