Defining parameters
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.j (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(756, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 324 | 12 | 312 |
Cusp forms | 252 | 12 | 240 |
Eisenstein series | 72 | 0 | 72 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(756, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
756.2.j.a | $6$ | $6.037$ | 6.0.309123.1 | None | \(0\) | \(0\) | \(-3\) | \(-3\) | \(q+(-1+\beta _{1}+\beta _{3})q^{5}-\beta _{3}q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\) |
756.2.j.b | $6$ | $6.037$ | 6.0.309123.1 | None | \(0\) | \(0\) | \(1\) | \(3\) | \(q+(-\beta _{1}+\beta _{5})q^{5}+(1-\beta _{4})q^{7}+(1-2\beta _{2}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(756, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(756, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)