Defining parameters
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(375\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1250, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 218 | 40 | 178 |
Cusp forms | 158 | 40 | 118 |
Eisenstein series | 60 | 0 | 60 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1250, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1250.2.b.a | $4$ | $9.981$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}-q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\) |
1250.2.b.b | $4$ | $9.981$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+(1-\beta _{2}+\cdots)q^{6}+\cdots\) |
1250.2.b.c | $8$ | $9.981$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{20}q^{2}+(-\zeta_{20}-\zeta_{20}^{2})q^{3}-q^{4}+\cdots\) |
1250.2.b.d | $8$ | $9.981$ | 8.0.\(\cdots\).2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{7}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{6}q^{6}+(2\beta _{4}+\cdots)q^{7}+\cdots\) |
1250.2.b.e | $8$ | $9.981$ | 8.0.\(\cdots\).15 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+\beta _{4}-\beta _{7})q^{6}+\cdots\) |
1250.2.b.f | $8$ | $9.981$ | 8.0.324000000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{5}q^{2}+(-\beta _{3}-\beta _{7})q^{3}-q^{4}-\beta _{2}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1250, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1250, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 2}\)