Defining parameters
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.q (of order \(11\) and degree \(10\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 23 \) |
Character field: | \(\Q(\zeta_{11})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(128\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(483, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 680 | 240 | 440 |
Cusp forms | 600 | 240 | 360 |
Eisenstein series | 80 | 0 | 80 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(483, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
483.2.q.a | $10$ | $3.857$ | \(\Q(\zeta_{22})\) | None | \(4\) | \(-1\) | \(1\) | \(-1\) | \(q+(-\zeta_{22}^{2}+\zeta_{22}^{3}+\zeta_{22}^{5}-\zeta_{22}^{6}+\cdots)q^{2}+\cdots\) |
483.2.q.b | $10$ | $3.857$ | \(\Q(\zeta_{22})\) | None | \(5\) | \(-1\) | \(-5\) | \(-1\) | \(q+(\zeta_{22}-\zeta_{22}^{2}-\zeta_{22}^{4}-\zeta_{22}^{6}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\) |
483.2.q.c | $20$ | $3.857$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-4\) | \(-2\) | \(-1\) | \(-2\) | \(q+(-\beta _{2}-\beta _{6})q^{2}+\beta _{12}q^{3}+(-\beta _{5}+\cdots)q^{4}+\cdots\) |
483.2.q.d | $60$ | $3.857$ | None | \(-1\) | \(6\) | \(-13\) | \(-6\) | ||
483.2.q.e | $60$ | $3.857$ | None | \(-1\) | \(6\) | \(5\) | \(6\) | ||
483.2.q.f | $80$ | $3.857$ | None | \(1\) | \(-8\) | \(13\) | \(8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(483, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)