Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.c (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(22\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{9}(25, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 46 | 26 | 20 |
Cusp forms | 34 | 22 | 12 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{9}^{\mathrm{new}}(25, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
25.9.c.a | $4$ | $10.184$ | \(\Q(i, \sqrt{141})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-26\beta _{1}q^{4}+282q^{6}+\cdots\) |
25.9.c.b | $6$ | $10.184$ | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) | None | \(2\) | \(72\) | \(0\) | \(2352\) | \(q+\beta _{3}q^{2}+(12+12\beta _{1}+\beta _{2}+\beta _{5})q^{3}+\cdots\) |
25.9.c.c | $12$ | $10.184$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(-\beta _{5}-\beta _{6}-\beta _{7})q^{3}+(281\beta _{1}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{9}^{\mathrm{old}}(25, [\chi])\) into lower level spaces
\( S_{9}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)