Defining parameters
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(42\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(36, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 40 | 16 | 24 |
Cusp forms | 32 | 14 | 18 |
Eisenstein series | 8 | 2 | 6 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(36, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
36.7.d.a | $1$ | $8.282$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(-8\) | \(0\) | \(-88\) | \(0\) | \(q-8q^{2}+2^{6}q^{4}-88q^{5}-2^{9}q^{8}+704q^{10}+\cdots\) |
36.7.d.b | $1$ | $8.282$ | \(\Q\) | \(\Q(\sqrt{-1}) \) | \(8\) | \(0\) | \(88\) | \(0\) | \(q+8q^{2}+2^{6}q^{4}+88q^{5}+2^{9}q^{8}+704q^{10}+\cdots\) |
36.7.d.c | $2$ | $8.282$ | \(\Q(\sqrt{-15}) \) | None | \(-4\) | \(0\) | \(-20\) | \(0\) | \(q+(-2-\beta )q^{2}+(-56+4\beta )q^{4}-10q^{5}+\cdots\) |
36.7.d.d | $4$ | $8.282$ | \(\Q(\sqrt{13}, \sqrt{-51})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(-38+\beta _{3})q^{4}+(-10\beta _{1}+\cdots)q^{5}+\cdots\) |
36.7.d.e | $6$ | $8.282$ | 6.0.50898483.1 | None | \(10\) | \(0\) | \(44\) | \(0\) | \(q+(2-\beta _{1})q^{2}+(26-\beta _{1}-\beta _{2})q^{4}+(7+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{7}^{\mathrm{old}}(36, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)