Defining parameters
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bv (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 640 | 80 | 560 |
Cusp forms | 512 | 80 | 432 |
Eisenstein series | 128 | 0 | 128 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
630.2.bv.a | $16$ | $5.031$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(-12\) | \(-8\) | \(q+\beta _{15}q^{2}+(\beta _{5}-\beta _{13})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\) |
630.2.bv.b | $16$ | $5.031$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(-12\) | \(-4\) | \(q-\beta _{6}q^{2}+(-\beta _{5}+\beta _{13})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\) |
630.2.bv.c | $16$ | $5.031$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(12\) | \(8\) | \(q+\beta _{13}q^{2}+(\beta _{11}-\beta _{14})q^{4}+(\beta _{5}-\beta _{6}+\cdots)q^{5}+\cdots\) |
630.2.bv.d | $32$ | $5.031$ | None | \(0\) | \(0\) | \(0\) | \(4\) |
Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(630, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)