Defining parameters
Level: | \( N \) | = | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 8002.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 7 \) | ||
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 irreducible Hecke orbits
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
\( S_{2}^{\mathrm{old}}(\Gamma_0(8002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(4001))\)\(^{\oplus 2}\)