Defining parameters
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.p (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 40 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(360\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(600, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 252 | 72 | 180 |
Cusp forms | 228 | 72 | 156 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(600, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
600.3.p.a | $8$ | $16.349$ | 8.0.22581504.2 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{4}q^{3}+(2-\beta _{3}+\cdots)q^{4}+\cdots\) |
600.3.p.b | $32$ | $16.349$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
600.3.p.c | $32$ | $16.349$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(600, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(600, [\chi]) \cong \)