Defining parameters
| Level: | \( N \) | \(=\) | \( 222 = 2 \cdot 3 \cdot 37 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 222.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 5 \) | ||
| Sturm bound: | \(76\) | ||
| Trace bound: | \(5\) | ||
| Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(222))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 42 | 5 | 37 |
| Cusp forms | 35 | 5 | 30 |
| Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(2\) | \(3\) | \(37\) | Fricke | Dim. |
|---|---|---|---|---|
| \(+\) | \(+\) | \(-\) | \(-\) | \(2\) |
| \(+\) | \(-\) | \(+\) | \(-\) | \(1\) |
| \(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
| \(-\) | \(-\) | \(-\) | \(-\) | \(1\) |
| Plus space | \(+\) | \(0\) | ||
| Minus space | \(-\) | \(5\) | ||
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(222))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 37 | |||||||
| 222.2.a.a | $1$ | $1.773$ | \(\Q\) | None | \(-1\) | \(-1\) | \(-4\) | \(3\) | $+$ | $+$ | $-$ | \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+3q^{7}+\cdots\) | |
| 222.2.a.b | $1$ | $1.773$ | \(\Q\) | None | \(-1\) | \(-1\) | \(2\) | \(0\) | $+$ | $+$ | $-$ | \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\) | |
| 222.2.a.c | $1$ | $1.773$ | \(\Q\) | None | \(-1\) | \(1\) | \(4\) | \(-1\) | $+$ | $-$ | $+$ | \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\) | |
| 222.2.a.d | $1$ | $1.773$ | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(3\) | $-$ | $+$ | $+$ | \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\) | |
| 222.2.a.e | $1$ | $1.773$ | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(-1\) | $-$ | $-$ | $-$ | \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\) | |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(222))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(222)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 2}\)