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
\( S_{2}^{\mathrm{old}}(\Gamma_0(4024)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\)\(^{\oplus 2}\)