Properties

Label 7056.2.bu
Level $7056$
Weight $2$
Character orbit 7056.bu
Rep. character $\chi_{7056}(4391,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $0$
Newform subspaces $0$
Sturm bound $2688$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7056.bu (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 0 \)
Sturm bound: \(2688\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7056, [\chi])\).

Total New Old
Modular forms 2816 0 2816
Cusp forms 2560 0 2560
Eisenstein series 256 0 256

Decomposition of \(S_{2}^{\mathrm{old}}(7056, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7056, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3528, [\chi])\)\(^{\oplus 2}\)