Defining parameters
Level: | \( N \) | \(=\) | \( 550 = 2 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 550.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(14\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 102 | 14 | 88 |
Cusp forms | 78 | 14 | 64 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
550.2.b.a | $2$ | $4.392$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots\) |
550.2.b.b | $2$ | $4.392$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}+i q^{3}-q^{4}-q^{6}-5 i q^{7}+\cdots\) |
550.2.b.c | $2$ | $4.392$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}-i q^{3}-q^{4}+q^{6}-i q^{7}+\cdots\) |
550.2.b.d | $2$ | $4.392$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}+4 i q^{7}+\cdots\) |
550.2.b.e | $2$ | $4.392$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}-i q^{8}+\cdots\) |
550.2.b.f | $4$ | $4.392$ | \(\Q(i, \sqrt{33})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+\beta _{3}q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(550, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)