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Properties

Label 2736.3.bk
Level $2736$
Weight $3$
Character orbit 2736.bk
Rep. character $\chi_{2736}(847,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $200$
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.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
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 1968 200 1768
Cusp forms 1872 200 1672
Eisenstein series 96 0 96

Trace form

\( 200 q + O(q^{10}) \) \( 200 q + 8 q^{13} - 72 q^{17} - 500 q^{25} - 80 q^{37} + 60 q^{41} - 1240 q^{49} - 24 q^{53} + 16 q^{61} + 192 q^{65} - 4 q^{73} + 192 q^{77} - 24 q^{85} + 72 q^{89} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{3}^{\mathrm{old}}(2736, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(912, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1368, [\chi])\)\(^{\oplus 2}\)