Defining parameters
Level: | \( N \) | \(=\) | \( 480 = 2^{5} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 480.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(480, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 208 | 48 | 160 |
Cusp forms | 176 | 48 | 128 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(480, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
480.3.c.a | $8$ | $13.079$ | 8.0.40960000.1 | \(\Q(\sqrt{-5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{5}q^{3}-5\beta _{1}q^{5}+(2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\) |
480.3.c.b | $16$ | $13.079$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{4}q^{3}-\beta _{7}q^{5}+(\beta _{3}-\beta _{4}+\beta _{8})q^{7}+\cdots\) |
480.3.c.c | $24$ | $13.079$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(480, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(480, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)