Defining parameters
| Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 4 \) |
| Character orbit: | \([\chi]\) | \(=\) | 84.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 2 \) | ||
| Sturm bound: | \(64\) | ||
| Trace bound: | \(3\) | ||
| Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(84))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 54 | 2 | 52 |
| Cusp forms | 42 | 2 | 40 |
| Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
| \(2\) | \(3\) | \(7\) | Fricke | Dim. |
|---|---|---|---|---|
| \(-\) | \(+\) | \(-\) | \(+\) | \(1\) |
| \(-\) | \(-\) | \(+\) | \(+\) | \(1\) |
| Plus space | \(+\) | \(2\) | ||
| Minus space | \(-\) | \(0\) | ||
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(84))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 7 | |||||||
| 84.4.a.a | \(1\) | \(4.956\) | \(\Q\) | None | \(0\) | \(-3\) | \(6\) | \(7\) | \(-\) | \(+\) | \(-\) | \(q-3q^{3}+6q^{5}+7q^{7}+9q^{9}+6^{2}q^{11}+\cdots\) | |
| 84.4.a.b | \(1\) | \(4.956\) | \(\Q\) | None | \(0\) | \(3\) | \(14\) | \(-7\) | \(-\) | \(-\) | \(+\) | \(q+3q^{3}+14q^{5}-7q^{7}+9q^{9}+4q^{11}+\cdots\) | |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(84))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(84)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)