Defining parameters
Level: | \( N \) | \(=\) | \( 528 = 2^{4} \cdot 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 528.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 11 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{5}(528, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 396 | 48 | 348 |
Cusp forms | 372 | 48 | 324 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{5}^{\mathrm{new}}(528, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
528.5.j.a | $8$ | $54.579$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(-36\) | \(0\) | \(q-\beta _{3}q^{3}+(-5+\beta _{3}+\beta _{6})q^{5}+(-3\beta _{1}+\cdots)q^{7}+\cdots\) |
528.5.j.b | $8$ | $54.579$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(-36\) | \(0\) | \(q-\beta _{1}q^{3}+(-4+2\beta _{1}-\beta _{2})q^{5}-\beta _{5}q^{7}+\cdots\) |
528.5.j.c | $8$ | $54.579$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(0\) | \(72\) | \(0\) | \(q-\beta _{1}q^{3}+(9-2\beta _{1}+\beta _{3})q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\) |
528.5.j.d | $24$ | $54.579$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{5}^{\mathrm{old}}(528, [\chi])\) into lower level spaces
\( S_{5}^{\mathrm{old}}(528, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)