Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.t (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 140 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(12\) | ||
Distinguishing \(T_p\): | \(3\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 152 | 112 |
Cusp forms | 216 | 136 | 80 |
Eisenstein series | 48 | 16 | 32 |
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.t.a | $4$ | $5.590$ | \(\Q(\zeta_{12})\) | None | \(-2\) | \(-6\) | \(0\) | \(-8\) | \(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-1+\cdots)q^{3}+\cdots\) |
700.2.t.b | $4$ | $5.590$ | \(\Q(\zeta_{12})\) | None | \(2\) | \(6\) | \(0\) | \(8\) | \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\) |
700.2.t.c | $32$ | $5.590$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
700.2.t.d | $32$ | $5.590$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
700.2.t.e | $64$ | $5.590$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)