Properties

Label 8400.2.dv
Level $8400$
Weight $2$
Character orbit 8400.dv
Rep. character $\chi_{8400}(1801,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $0$
Newform subspaces $0$
Sturm bound $3840$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8400.dv (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 0 \)
Sturm bound: \(3840\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8400, [\chi])\).

Total New Old
Modular forms 3936 0 3936
Cusp forms 3744 0 3744
Eisenstein series 192 0 192

Decomposition of \(S_{2}^{\mathrm{old}}(8400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(840, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1400, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(4200, [\chi])\)\(^{\oplus 2}\)