Defining parameters
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 228 | 12 | 216 |
Cusp forms | 132 | 12 | 120 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
450.2.f.a | $4$ | $3.593$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(-12\) | \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-3+3\zeta_{8}^{2})q^{7}+\cdots\) |
450.2.f.b | $4$ | $3.593$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{7}+\cdots\) |
450.2.f.c | $4$ | $3.593$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(12\) | \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(3-3\zeta_{8}^{2})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(450, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)