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Properties

Label 1216.2.bm
Level $1216$
Weight $2$
Character orbit 1216.bm
Rep. character $\chi_{1216}(127,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $228$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.bm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1216, [\chi])\).

Total New Old
Modular forms 1032 252 780
Cusp forms 888 228 660
Eisenstein series 144 24 120

Trace form

\( 228 q + 12 q^{5} - 12 q^{9} + O(q^{10}) \) \( 228 q + 12 q^{5} - 12 q^{9} + 36 q^{13} - 12 q^{17} + 54 q^{21} - 12 q^{25} + 12 q^{29} - 30 q^{33} - 36 q^{41} + 6 q^{45} + 72 q^{49} + 12 q^{53} - 12 q^{57} + 60 q^{61} - 18 q^{65} - 126 q^{69} - 12 q^{73} + 252 q^{77} - 18 q^{81} - 84 q^{85} - 12 q^{89} + 42 q^{93} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1216, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1216, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1216, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(608, [\chi])\)\(^{\oplus 2}\)