Defining parameters
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 736 | 80 | 656 |
Cusp forms | 608 | 80 | 528 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)