Defining parameters
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 44 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 88 | 72 | 16 |
Cusp forms | 80 | 72 | 8 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
572.2.e.a | $8$ | $4.567$ | 8.0.342102016.5 | None | \(0\) | \(0\) | \(-12\) | \(0\) | \(q-\beta _{4}q^{2}+(-\beta _{3}-\beta _{5}+\beta _{7})q^{4}+(-2+\cdots)q^{5}+\cdots\) |
572.2.e.b | $64$ | $4.567$ | None | \(0\) | \(0\) | \(12\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 2}\)