Defining parameters
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 12 \) | ||
Sturm bound: | \(960\) | ||
Trace bound: | \(43\) | ||
Distinguishing \(T_p\): | \(11\), \(13\), \(17\), \(37\), \(41\), \(43\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 516 | 50 | 466 |
Cusp forms | 444 | 50 | 394 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)