Properties

Label 2736.3.bs
Level $2736$
Weight $3$
Character orbit 2736.bs
Rep. character $\chi_{2736}(1633,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $476$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2736.bs (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2736, [\chi])\).

Total New Old
Modular forms 1944 484 1460
Cusp forms 1896 476 1420
Eisenstein series 48 8 40

Trace form

\( 476q - 2q^{5} + 2q^{7} + 4q^{9} + O(q^{10}) \) \( 476q - 2q^{5} + 2q^{7} + 4q^{9} + 2q^{11} + 40q^{17} + 4q^{19} + 2q^{23} - 1152q^{25} - 92q^{35} + 22q^{39} + 98q^{43} + 46q^{45} + 2q^{47} - 1584q^{49} - 92q^{55} - 44q^{57} - 2q^{61} - 238q^{63} + 40q^{73} + 194q^{77} + 260q^{81} + 2q^{83} - 52q^{85} + 246q^{87} - 22q^{93} + 242q^{95} - 94q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2736, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2736, [\chi])\) into lower level spaces

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