Defining parameters
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(432\) | ||
Trace bound: | \(8\) | ||
Distinguishing \(T_p\): | \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 228 | 64 | 164 |
Cusp forms | 204 | 64 | 140 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1080.2.k.a | $12$ | $8.624$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{9}q^{2}-\beta _{8}q^{4}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots\) |
1080.2.k.b | $16$ | $8.624$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{9}q^{2}-\beta _{2}q^{4}-\beta _{7}q^{5}-\beta _{14}q^{7}+\cdots\) |
1080.2.k.c | $16$ | $8.624$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{8}q^{5}-\beta _{11}q^{7}+\cdots\) |
1080.2.k.d | $20$ | $8.624$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+\beta _{4}q^{4}-\beta _{6}q^{5}-\beta _{12}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(216, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(360, [\chi])\)\(^{\oplus 2}\)