Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(700, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 276 | 24 | 252 |
Cusp forms | 204 | 24 | 180 |
Eisenstein series | 72 | 0 | 72 |
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.r.a | $4$ | $5.590$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}+(\zeta_{12}+2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\) |
700.2.r.b | $4$ | $5.590$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\) |
700.2.r.c | $4$ | $5.590$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots\) |
700.2.r.d | $12$ | $5.590$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{4}-\beta _{10})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(700, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)