Defining parameters
Level: | \( N \) | \(=\) | \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2178.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 3 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(1188\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(5\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(2178, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 840 | 74 | 766 |
Cusp forms | 744 | 74 | 670 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(2178, [\chi])\) into newform subspaces
Decomposition of \(S_{3}^{\mathrm{old}}(2178, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(2178, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(726, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1089, [\chi])\)\(^{\oplus 2}\)