Defining parameters
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.n (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(160\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 336 | 112 | 224 |
Cusp forms | 304 | 112 | 192 |
Eisenstein series | 32 | 0 | 32 |
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.n.a | $4$ | $4.192$ | \(\Q(\zeta_{10})\) | None | \(3\) | \(1\) | \(0\) | \(-4\) | \(q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots\) |
525.2.n.b | $20$ | $4.192$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-2\) | \(5\) | \(5\) | \(-20\) | \(q+\beta _{10}q^{2}+\beta _{4}q^{3}+(\beta _{1}-2\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\) |
525.2.n.c | $24$ | $4.192$ | None | \(1\) | \(-6\) | \(-1\) | \(24\) | ||
525.2.n.d | $32$ | $4.192$ | None | \(1\) | \(-8\) | \(-3\) | \(-32\) | ||
525.2.n.e | $32$ | $4.192$ | None | \(1\) | \(8\) | \(7\) | \(32\) |
Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)