Defining parameters
Level: | \( N \) | = | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 8023.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 5 \) | ||
Sturm bound: | \(1368\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8023))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 686 | 653 | 33 |
Cusp forms | 683 | 653 | 30 |
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.
\(71\) | \(113\) | Fricke | Dim. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(161\) |
\(+\) | \(-\) | \(-\) | \(172\) |
\(-\) | \(+\) | \(-\) | \(165\) |
\(-\) | \(-\) | \(+\) | \(155\) |
Plus space | \(+\) | \(316\) | |
Minus space | \(-\) | \(337\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 71 | 113 | |||||||
8023.2.a.a | \(3\) | \(64.064\) | \(\Q(\zeta_{14})^+\) | None | \(2\) | \(3\) | \(-1\) | \(-2\) | \(+\) | \(+\) | \(q+(1-\beta _{1})q^{2}+(2\beta _{1}-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\) | |
8023.2.a.b | \(155\) | \(64.064\) | None | \(-21\) | \(-16\) | \(-26\) | \(-40\) | \(-\) | \(-\) | |||
8023.2.a.c | \(158\) | \(64.064\) | None | \(-24\) | \(-23\) | \(-31\) | \(-2\) | \(+\) | \(+\) | |||
8023.2.a.d | \(165\) | \(64.064\) | None | \(22\) | \(18\) | \(28\) | \(24\) | \(-\) | \(+\) | |||
8023.2.a.e | \(172\) | \(64.064\) | None | \(24\) | \(18\) | \(28\) | \(4\) | \(+\) | \(-\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8023))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(71))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(113))\)\(^{\oplus 2}\)