Properties

Label 8400.2.jr
Level $8400$
Weight $2$
Character orbit 8400.jr
Rep. character $\chi_{8400}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
Sturm bound $3840$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 8400 = 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8400.jr (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 700 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(3840\)

Dimensions

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

Total New Old
Modular forms 15552 1920 13632
Cusp forms 15168 1920 13248
Eisenstein series 384 0 384

Decomposition of \(S_{2}^{\mathrm{new}}(8400, [\chi])\) into newform subspaces

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

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

\( S_{2}^{\mathrm{old}}(8400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2800, [\chi])\)\(^{\oplus 2}\)