Defining parameters
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(390, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 184 | 28 | 156 |
Cusp forms | 152 | 28 | 124 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(390, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
390.2.j.a | $12$ | $3.114$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(-12\) | \(0\) | \(0\) | \(0\) | \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\) |
390.2.j.b | $16$ | $3.114$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(16\) | \(0\) | \(0\) | \(0\) | \(q+q^{2}+\beta _{8}q^{3}+q^{4}+\beta _{14}q^{5}+\beta _{8}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(390, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)