Properties

Label 1296.3.h
Level $1296$
Weight $3$
Character orbit 1296.h
Rep. character $\chi_{1296}(809,\cdot)$
Character field $\Q$
Dimension $0$
Newform subspaces $0$
Sturm bound $648$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1296.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 0 \)
Sturm bound: \(648\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1296, [\chi])\).

Total New Old
Modular forms 456 0 456
Cusp forms 408 0 408
Eisenstein series 48 0 48

Decomposition of \(S_{3}^{\mathrm{old}}(1296, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1296, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(648, [\chi])\)\(^{\oplus 2}\)