Defining parameters
Level: | \( N \) | \(=\) | \( 430 = 2 \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 430.q (of order \(21\) and degree \(12\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 43 \) |
Character field: | \(\Q(\zeta_{21})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(430, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 840 | 192 | 648 |
Cusp forms | 744 | 192 | 552 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(430, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
430.2.q.a | $36$ | $3.434$ | None | \(-6\) | \(5\) | \(3\) | \(1\) | ||
430.2.q.b | $48$ | $3.434$ | None | \(-8\) | \(-1\) | \(-4\) | \(-7\) | ||
430.2.q.c | $48$ | $3.434$ | None | \(8\) | \(-7\) | \(4\) | \(-3\) | ||
430.2.q.d | $60$ | $3.434$ | None | \(10\) | \(-1\) | \(-5\) | \(1\) |
Decomposition of \(S_{2}^{\mathrm{old}}(430, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(430, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(86, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)