Defining parameters
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.n (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(48\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 72 | 20 | 52 |
Cusp forms | 56 | 20 | 36 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
105.3.n.a | $8$ | $2.861$ | 8.0.\(\cdots\).16 | None | \(2\) | \(-12\) | \(0\) | \(-16\) | \(q+\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\) |
105.3.n.b | $12$ | $2.861$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(2\) | \(18\) | \(0\) | \(22\) | \(q+(-\beta _{2}-\beta _{10})q^{2}+(2+\beta _{3})q^{3}+(4\beta _{3}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)