Properties

Label 3072.2.bd
Level $3072$
Weight $2$
Character orbit 3072.bd
Rep. character $\chi_{3072}(25,\cdot)$
Character field $\Q(\zeta_{128})$
Dimension $0$
Newform subspaces $0$
Sturm bound $1024$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 3072 = 2^{10} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3072.bd (of order \(128\) and degree \(64\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 512 \)
Character field: \(\Q(\zeta_{128})\)
Newform subspaces: \( 0 \)
Sturm bound: \(1024\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3072, [\chi])\).

Total New Old
Modular forms 33024 0 33024
Cusp forms 32512 0 32512
Eisenstein series 512 0 512

Decomposition of \(S_{2}^{\mathrm{old}}(3072, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3072, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(512, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1536, [\chi])\)\(^{\oplus 2}\)