Defining parameters
Level: | \( N \) | \(=\) | \( 250 = 2 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 250.d (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(75\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(250, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 188 | 28 | 160 |
Cusp forms | 108 | 28 | 80 |
Eisenstein series | 80 | 0 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(250, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
250.2.d.a | $4$ | $1.996$ | \(\Q(\zeta_{10})\) | None | \(-1\) | \(1\) | \(0\) | \(12\) | \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\) |
250.2.d.b | $8$ | $1.996$ | \(\Q(\zeta_{20})\) | None | \(-2\) | \(2\) | \(0\) | \(-16\) | \(q-\zeta_{20}q^{2}+(-\zeta_{20}^{3}+\zeta_{20}^{5})q^{3}+\zeta_{20}^{3}q^{4}+\cdots\) |
250.2.d.c | $8$ | $1.996$ | \(\Q(\zeta_{20})\) | None | \(2\) | \(-2\) | \(0\) | \(16\) | \(q+\zeta_{20}^{4}q^{2}+(-\zeta_{20}+\zeta_{20}^{2})q^{3}-\zeta_{20}q^{4}+\cdots\) |
250.2.d.d | $8$ | $1.996$ | 8.0.58140625.2 | None | \(2\) | \(3\) | \(0\) | \(-4\) | \(q+(1-\beta _{2}-\beta _{3}-\beta _{6})q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(250, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(250, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)