Defining parameters
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(200, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 102 | 14 | 88 |
Cusp forms | 78 | 14 | 64 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(200, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
200.4.c.a | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+5iq^{3}+9iq^{7}-73q^{9}-2^{4}q^{11}+\cdots\) |
200.4.c.b | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+9iq^{3}-26iq^{7}-54q^{9}-59q^{11}+\cdots\) |
200.4.c.c | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3iq^{3}-17iq^{7}-9q^{9}+2^{4}q^{11}+\cdots\) |
200.4.c.d | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+5iq^{3}-2iq^{7}+2q^{9}+39q^{11}+\cdots\) |
200.4.c.e | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{3}+12iq^{7}+11q^{9}-44q^{11}+\cdots\) |
200.4.c.f | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{3}-8iq^{7}+11q^{9}+6^{2}q^{11}+\cdots\) |
200.4.c.g | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}+6iq^{7}+26q^{9}-19q^{11}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(200, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)