Defining parameters
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.f (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 9 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 152 | 36 | 116 |
Cusp forms | 136 | 36 | 100 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
126.4.f.a | $6$ | $7.434$ | 6.0.309123.1 | None | \(6\) | \(-12\) | \(-9\) | \(-21\) | \(q+2\beta _{3}q^{2}+(-2-\beta _{1}+\beta _{5})q^{3}+(-4+\cdots)q^{4}+\cdots\) |
126.4.f.b | $8$ | $7.434$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(-8\) | \(9\) | \(1\) | \(28\) | \(q+(-2-2\beta _{1})q^{2}+(2+\beta _{1}-\beta _{2})q^{3}+\cdots\) |
126.4.f.c | $10$ | $7.434$ | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) | None | \(10\) | \(4\) | \(1\) | \(35\) | \(q+(2-2\beta _{3})q^{2}-\beta _{2}q^{3}-4\beta _{3}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\) |
126.4.f.d | $12$ | $7.434$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(-12\) | \(-7\) | \(-9\) | \(-42\) | \(q+(-2+2\beta _{4})q^{2}+(-\beta _{4}+\beta _{5})q^{3}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)