Defining parameters
Level: | \( N \) | \(=\) | \( 875 = 5^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 875.n (of order \(10\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{10})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(200\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(875, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 440 | 184 | 256 |
Cusp forms | 360 | 184 | 176 |
Eisenstein series | 80 | 0 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(875, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
875.2.n.a | $8$ | $6.987$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\cdots\) |
875.2.n.b | $56$ | $6.987$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
875.2.n.c | $56$ | $6.987$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
875.2.n.d | $64$ | $6.987$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(875, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(875, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)