Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.bv (of order \(60\) and degree \(16\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 175 \) |
Character field: | \(\Q(\zeta_{60})\) | ||
Newform subspaces: | \( 1 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2016 | 320 | 1696 |
Cusp forms | 1824 | 320 | 1504 |
Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(700, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
700.2.bv.a | $320$ | $5.590$ | None | \(0\) | \(0\) | \(-6\) | \(-2\) |
Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)