Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 24 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(320\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(384, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 272 | 64 | 208 |
Cusp forms | 240 | 64 | 176 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(384, [\chi])\) into newform subspaces
Decomposition of \(S_{5}^{\mathrm{old}}(384, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(384, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)