Defining parameters
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.m (of order \(5\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 25 \) |
Character field: | \(\Q(\zeta_{5})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(300, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 264 | 16 | 248 |
Cusp forms | 216 | 16 | 200 |
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.m.a | $8$ | $2.396$ | \(\Q(\zeta_{15})\) | None | \(0\) | \(-2\) | \(5\) | \(-8\) | \(q+\zeta_{15}^{5}q^{3}+(-1-2\zeta_{15}^{2}-\zeta_{15}^{3}+\cdots)q^{5}+\cdots\) |
300.2.m.b | $8$ | $2.396$ | 8.0.26265625.1 | None | \(0\) | \(2\) | \(-5\) | \(8\) | \(q+\beta _{3}q^{3}+(-1+\beta _{6}-\beta _{7})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(300, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)