Defining parameters
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 184 | 48 | 136 |
Cusp forms | 136 | 48 | 88 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
525.2.m.a | $8$ | $4.192$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\) |
525.2.m.b | $16$ | $4.192$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q-\beta _{5}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{7}-\beta _{11}+\cdots)q^{4}+\cdots\) |
525.2.m.c | $24$ | $4.192$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)