Defining parameters
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 13 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
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 | 90 | 14 | 76 |
Cusp forms | 78 | 14 | 64 |
Eisenstein series | 12 | 0 | 12 |
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.f.a | $2$ | $4.567$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+4iq^{7}-3q^{9}-iq^{11}+(-3+2i)q^{13}+\cdots\) |
572.2.f.b | $4$ | $4.567$ | \(\Q(i, \sqrt{21})\) | None | \(0\) | \(2\) | \(0\) | \(0\) | \(q+(1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2})q^{7}+(3-\beta _{3})q^{9}+\cdots\) |
572.2.f.c | $8$ | $4.567$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(-2\) | \(0\) | \(0\) | \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{5}+\beta _{6}-\beta _{7})q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)