Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{36}(25, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 90 | 54 | 36 |
Cusp forms | 84 | 52 | 32 |
Eisenstein series | 6 | 2 | 4 |
Trace form
Decomposition of \(S_{36}^{\mathrm{new}}(25, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
25.36.b.a | $6$ | $193.988$ | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(186\beta _{1}-\beta _{2})q^{2}+(139834\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\) |
25.36.b.b | $10$ | $193.988$ | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(15\beta _{5}+\beta _{6})q^{2}+(-8312\beta _{5}-204\beta _{6}+\cdots)q^{3}+\cdots\) |
25.36.b.c | $12$ | $193.988$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(214\beta _{1}-1573\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots\) |
25.36.b.d | $24$ | $193.988$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{36}^{\mathrm{old}}(25, [\chi])\) into lower level spaces
\( S_{36}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{36}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)