Defining parameters
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.p (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 105 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(224\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\), \(13\), \(257\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(735, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 176 | 80 |
Cusp forms | 192 | 144 | 48 |
Eisenstein series | 64 | 32 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(735, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
735.2.p.a | $8$ | $5.869$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{2}+(-1+\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\) |
735.2.p.b | $8$ | $5.869$ | 8.0.\(\cdots\).2 | \(\Q(\sqrt{-35}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{6}q^{3}+(2+2\beta _{4})q^{4}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\) |
735.2.p.c | $8$ | $5.869$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{2}+(1-\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\) |
735.2.p.d | $16$ | $5.869$ | 16.0.\(\cdots\).5 | \(\Q(\sqrt{-15}) \) | \(0\) | \(-24\) | \(0\) | \(0\) | \(q+(-\beta _{2}+\beta _{7})q^{2}+(-1+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\) |
735.2.p.e | $16$ | $5.869$ | 16.0.\(\cdots\).5 | \(\Q(\sqrt{-15}) \) | \(0\) | \(24\) | \(0\) | \(0\) | \(q+(-\beta _{2}+\beta _{7})q^{2}+(1-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\) |
735.2.p.f | $24$ | $5.869$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
735.2.p.g | $64$ | $5.869$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(735, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)