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 | \(0\) | \(0\) | \(0\) | \(0\) | \(q+5\beta q^{3}+9\beta q^{7}-73 q^{9}-16 q^{11}+\cdots\) |
200.4.c.b | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+9 i q^{3}-26 i q^{7}-54 q^{9}-59 q^{11}+\cdots\) |
200.4.c.c | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3\beta q^{3}-17\beta q^{7}-9 q^{9}+16 q^{11}+\cdots\) |
200.4.c.d | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+5 i q^{3}-2 i q^{7}+2 q^{9}+39 q^{11}+\cdots\) |
200.4.c.e | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\beta q^{3}+12\beta q^{7}+11 q^{9}-44 q^{11}+\cdots\) |
200.4.c.f | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2\beta q^{3}-8\beta q^{7}+11 q^{9}+36 q^{11}+\cdots\) |
200.4.c.g | $2$ | $11.800$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+i q^{3}+6 i q^{7}+26 q^{9}-19 q^{11}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(200, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(200, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)