Properties

Label 6864.2.ka
Level $6864$
Weight $2$
Character orbit 6864.ka
Rep. character $\chi_{6864}(49,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1344$
Sturm bound $2688$

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Defining parameters

Level: \( N \) \(=\) \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6864.ka (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(2688\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(6864, [\chi])\).

Total New Old
Modular forms 10944 1344 9600
Cusp forms 10560 1344 9216
Eisenstein series 384 0 384

Decomposition of \(S_{2}^{\mathrm{new}}(6864, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(6864, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(6864, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(858, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1716, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3432, [\chi])\)\(^{\oplus 2}\)