Defining parameters
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.l (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(390, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 184 | 48 | 136 |
Cusp forms | 152 | 48 | 104 |
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.l.a | $4$ | $3.114$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\) |
390.2.l.b | $4$ | $3.114$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(8\) | \(q+\zeta_{8}q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\) |
390.2.l.c | $20$ | $3.114$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{9}q^{2}+\beta _{1}q^{3}-\beta _{11}q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\) |
390.2.l.d | $20$ | $3.114$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q+\beta _{4}q^{2}+\beta _{12}q^{3}+\beta _{11}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(390, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)