Defining parameters
Level: | \( N \) | \(=\) | \( 435 = 3 \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 435.u (of order \(7\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 29 \) |
Character field: | \(\Q(\zeta_{7})\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 384 | 120 | 264 |
Cusp forms | 336 | 120 | 216 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
435.2.u.a | $30$ | $3.473$ | None | \(1\) | \(-5\) | \(5\) | \(0\) | ||
435.2.u.b | $30$ | $3.473$ | None | \(1\) | \(5\) | \(-5\) | \(4\) | ||
435.2.u.c | $30$ | $3.473$ | None | \(3\) | \(-5\) | \(-5\) | \(4\) | ||
435.2.u.d | $30$ | $3.473$ | None | \(3\) | \(5\) | \(5\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)