Defining parameters
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 92 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(2304\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(5520, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1176 | 96 | 1080 |
Cusp forms | 1128 | 96 | 1032 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(5520, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
5520.2.be.a | $16$ | $44.077$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\beta _{10}q^{3}+\beta _{10}q^{5}+(-1-\beta _{4})q^{7}+\cdots\) |
5520.2.be.b | $16$ | $44.077$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{10}q^{3}+\beta _{10}q^{5}+(1+\beta _{4})q^{7}-q^{9}+\cdots\) |
5520.2.be.c | $32$ | $44.077$ | None | \(0\) | \(0\) | \(0\) | \(-8\) | ||
5520.2.be.d | $32$ | $44.077$ | None | \(0\) | \(0\) | \(0\) | \(8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(5520, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(5520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2760, [\chi])\)\(^{\oplus 2}\)