Defining parameters
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.j (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(7\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 144 | 36 | 108 |
Cusp forms | 96 | 36 | 60 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(300, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
300.2.j.a | $8$ | $2.396$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{5})q^{2}+\zeta_{24}q^{3}+\cdots\) |
300.2.j.b | $8$ | $2.396$ | 8.0.157351936.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{2}+\beta _{4})q^{2}+\beta _{6}q^{3}+(\beta _{3}+\beta _{5})q^{4}+\cdots\) |
300.2.j.c | $8$ | $2.396$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{24}-\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+(\zeta_{24}^{2}+\cdots)q^{4}+\cdots\) |
300.2.j.d | $12$ | $2.396$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{8}+\beta _{9})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)