Properties

Label 2736.2.cn
Level $2736$
Weight $2$
Character orbit 2736.cn
Rep. character $\chi_{2736}(113,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $236$
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.cn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 984 244 740
Cusp forms 936 236 700
Eisenstein series 48 8 40

Trace form

\( 236q - 6q^{5} + 2q^{7} - 8q^{9} + O(q^{10}) \) \( 236q - 6q^{5} + 2q^{7} - 8q^{9} + 6q^{11} + 4q^{19} + 6q^{23} + 108q^{25} + 10q^{39} + 14q^{43} - 14q^{45} + 6q^{47} - 108q^{49} + 28q^{55} - 2q^{57} - 2q^{61} - 46q^{63} + 16q^{73} - 6q^{77} + 32q^{81} + 6q^{83} + 8q^{85} - 30q^{87} - 10q^{93} - 36q^{95} + 38q^{99} + O(q^{100}) \)

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

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