Defining parameters
Level: | \( N \) | \(=\) | \( 465 = 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 465.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 465 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\), \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(465, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 68 | 0 |
Cusp forms | 60 | 60 | 0 |
Eisenstein series | 8 | 8 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(465, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
465.2.g.a | $4$ | $3.713$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q+\beta _{3}q^{2}+(-2-\beta _{2})q^{3}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\) |
465.2.g.b | $4$ | $3.713$ | \(\Q(\sqrt{-3}, \sqrt{5})\) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+3q^{4}-\beta _{1}q^{5}+\beta _{3}q^{6}+\cdots\) |
465.2.g.c | $4$ | $3.713$ | \(\Q(\sqrt{2}, \sqrt{-3})\) | None | \(0\) | \(6\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+(2+\beta _{2})q^{3}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\) |
465.2.g.d | $8$ | $3.713$ | 8.0.\(\cdots\).6 | \(\Q(\sqrt{-155}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-2q^{4}+\beta _{4}q^{5}+\beta _{2}q^{9}-2\beta _{1}q^{12}+\cdots\) |
465.2.g.e | $8$ | $3.713$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{2}-\zeta_{24}^{5}q^{3}+q^{4}+(-\zeta_{24}+\cdots)q^{5}+\cdots\) |
465.2.g.f | $32$ | $3.713$ | None | \(0\) | \(0\) | \(0\) | \(0\) |