Defining parameters
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(2001\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8002))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1002 | 333 | 669 |
Cusp forms | 999 | 333 | 666 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(4001\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(89\) |
\(+\) | \(-\) | $-$ | \(77\) |
\(-\) | \(+\) | $-$ | \(95\) |
\(-\) | \(-\) | $+$ | \(72\) |
Plus space | \(+\) | \(161\) | |
Minus space | \(-\) | \(172\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8002))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 4001 | |||||||
8002.2.a.a | $1$ | $63.896$ | \(\Q\) | None | \(1\) | \(-1\) | \(1\) | \(0\) | $-$ | $-$ | \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\) | |
8002.2.a.b | $1$ | $63.896$ | \(\Q\) | None | \(1\) | \(0\) | \(0\) | \(0\) | $-$ | $-$ | \(q+q^{2}+q^{4}+q^{8}-3q^{9}-2q^{11}+4q^{13}+\cdots\) | |
8002.2.a.c | $1$ | $63.896$ | \(\Q\) | None | \(1\) | \(2\) | \(-2\) | \(0\) | $-$ | $-$ | \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\) | |
8002.2.a.d | $69$ | $63.896$ | None | \(69\) | \(-25\) | \(-33\) | \(-19\) | $-$ | $-$ | |||
8002.2.a.e | $77$ | $63.896$ | None | \(-77\) | \(10\) | \(18\) | \(21\) | $+$ | $-$ | |||
8002.2.a.f | $89$ | $63.896$ | None | \(-89\) | \(-12\) | \(-18\) | \(-27\) | $+$ | $+$ | |||
8002.2.a.g | $95$ | $63.896$ | None | \(95\) | \(24\) | \(36\) | \(21\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8002))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\)\(^{\oplus 2}\)