Defining parameters
| Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 400.c (of order \(2\) and degree \(1\)) |
| Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 4 \) | ||
| Sturm bound: | \(120\) | ||
| Trace bound: | \(9\) | ||
| Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(400, [\chi])\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 78 | 10 | 68 |
| Cusp forms | 42 | 8 | 34 |
| Eisenstein series | 36 | 2 | 34 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(400, [\chi])\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | $q$-expansion | |||
|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | ||||||
| 400.2.c.a | \(2\) | \(3.194\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+3iq^{3}+2iq^{7}-6q^{9}-q^{11}+4iq^{13}+\cdots\) |
| 400.2.c.b | \(2\) | \(3.194\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}+iq^{7}-q^{9}+iq^{13}+3iq^{17}+\cdots\) |
| 400.2.c.c | \(2\) | \(3.194\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-2iq^{7}+2q^{9}+3q^{11}+4iq^{13}+\cdots\) |
| 400.2.c.d | \(2\) | \(3.194\) | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{7}+3q^{9}-4q^{11}+iq^{13}+iq^{17}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(400, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)