Defining parameters
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(16\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(35, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 16 | 12 |
Cusp forms | 20 | 16 | 4 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(35, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
35.4.e.a | $2$ | $2.065$ | \(\Q(\sqrt{-3}) \) | None | \(-3\) | \(2\) | \(-5\) | \(-28\) | \(q-3\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\) |
35.4.e.b | $4$ | $2.065$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(6\) | \(2\) | \(-10\) | \(22\) | \(q+(\beta _{1}-3\beta _{2}+\beta _{3})q^{2}+(1+3\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\) |
35.4.e.c | $10$ | $2.065$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(-1\) | \(8\) | \(25\) | \(-62\) | \(q+(\beta _{1}-\beta _{2})q^{2}+(-\beta _{3}-\beta _{5}+2\beta _{6}+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(35, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(35, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)