Defining parameters
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.e (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(60\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(150, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 12 | 72 |
Cusp forms | 36 | 12 | 24 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(150, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
150.2.e.a | $4$ | $1.198$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(4\) | \(0\) | \(4\) | \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\) |
150.2.e.b | $8$ | $1.198$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(-2\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(150, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)