Properties

Label 2736.2.q
Level $2736$
Weight $2$
Character orbit 2736.q
Rep. character $\chi_{2736}(913,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $216$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2736, [\chi])\).

Total New Old
Modular forms 984 216 768
Cusp forms 936 216 720
Eisenstein series 48 0 48

Trace form

\( 216q + O(q^{10}) \) \( 216q - 12q^{11} - 12q^{15} + 8q^{21} + 12q^{23} - 108q^{25} + 36q^{27} - 8q^{29} + 48q^{35} + 60q^{39} - 16q^{45} + 32q^{47} - 108q^{49} - 4q^{51} - 12q^{59} - 40q^{63} - 24q^{69} - 48q^{71} - 12q^{75} - 16q^{77} - 8q^{81} - 56q^{83} - 60q^{87} - 16q^{89} - 8q^{93} + 16q^{95} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)