Defining parameters
| Level: | \( N \) | = | \( 4024 = 2^{3} \cdot 503 \) |
| Weight: | \( k \) | = | \( 2 \) |
| Character orbit: | \([\chi]\) | = | 4024.a (trivial) |
| Character field: | \(\Q\) | ||
| Newform subspaces: | \( 7 \) | ||
| Sturm bound: | \(1008\) | ||
| Trace bound: | \(7\) | ||
| Distinguishing \(T_p\): | \(3\), \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4024))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 508 | 126 | 382 |
| Cusp forms | 501 | 126 | 375 |
| 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.
| \(2\) | \(503\) | Fricke | Dim. |
|---|---|---|---|
| \(+\) | \(+\) | \(+\) | \(29\) |
| \(+\) | \(-\) | \(-\) | \(34\) |
| \(-\) | \(+\) | \(-\) | \(34\) |
| \(-\) | \(-\) | \(+\) | \(29\) |
| Plus space | \(+\) | \(58\) | |
| Minus space | \(-\) | \(68\) | |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\) into newform subspaces
| Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 503 | |||||||
| 4024.2.a.a | \(1\) | \(32.132\) | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(-5\) | \(-\) | \(+\) | \(q-q^{3}-5q^{7}-2q^{9}-5q^{11}+q^{13}+\cdots\) | |
| 4024.2.a.b | \(1\) | \(32.132\) | \(\Q\) | None | \(0\) | \(-1\) | \(0\) | \(1\) | \(-\) | \(-\) | \(q-q^{3}+q^{7}-2q^{9}-5q^{11}+3q^{13}+\cdots\) | |
| 4024.2.a.c | \(1\) | \(32.132\) | \(\Q\) | None | \(0\) | \(-1\) | \(2\) | \(1\) | \(+\) | \(-\) | \(q-q^{3}+2q^{5}+q^{7}-2q^{9}+3q^{11}+\cdots\) | |
| 4024.2.a.d | \(28\) | \(32.132\) | None | \(0\) | \(2\) | \(-12\) | \(0\) | \(-\) | \(-\) | |||
| 4024.2.a.e | \(29\) | \(32.132\) | None | \(0\) | \(-7\) | \(-4\) | \(-13\) | \(+\) | \(+\) | |||
| 4024.2.a.f | \(33\) | \(32.132\) | None | \(0\) | \(-2\) | \(12\) | \(4\) | \(-\) | \(+\) | |||
| 4024.2.a.g | \(33\) | \(32.132\) | None | \(0\) | \(10\) | \(0\) | \(12\) | \(+\) | \(-\) | |||
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4024))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\)\(^{\oplus 2}\)