Defining parameters
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.bl (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3528, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1472 | 80 | 1392 |
Cusp forms | 1216 | 80 | 1136 |
Eisenstein series | 256 | 0 | 256 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3528, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3528.2.bl.a | $16$ | $28.171$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{4}-\beta _{10})q^{5}+(\beta _{2}-\beta _{11}+\beta _{12}+\cdots)q^{11}+\cdots\) |
3528.2.bl.b | $16$ | $28.171$ | \(\Q(\zeta_{48})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{48}^{4}q^{5}+(\zeta_{48}-\zeta_{48}^{3}-\zeta_{48}^{5}+\cdots)q^{11}+\cdots\) |
3528.2.bl.c | $16$ | $28.171$ | \(\Q(\zeta_{48})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{48}^{4}-\zeta_{48}^{15})q^{5}+(\zeta_{48}-\zeta_{48}^{5}+\cdots)q^{11}+\cdots\) |
3528.2.bl.d | $32$ | $28.171$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3528, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3528, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)