Defining parameters
Level: | \( N \) | = | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 6026.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 13 \) | ||
Sturm bound: | \(1584\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6026))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 796 | 241 | 555 |
Cusp forms | 789 | 241 | 548 |
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.
\(2\) | \(23\) | \(131\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(25\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(36\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(34\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(25\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(37\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(23\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(20\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(41\) |
Plus space | \(+\) | \(93\) | ||
Minus space | \(-\) | \(148\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 23 | 131 | |||||||
6026.2.a.a | \(1\) | \(48.118\) | \(\Q\) | None | \(-1\) | \(0\) | \(0\) | \(0\) | \(+\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}-q^{8}-3q^{9}+2q^{11}-2q^{13}+\cdots\) | |
6026.2.a.b | \(1\) | \(48.118\) | \(\Q\) | None | \(-1\) | \(0\) | \(3\) | \(-2\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{9}+\cdots\) | |
6026.2.a.c | \(1\) | \(48.118\) | \(\Q\) | None | \(1\) | \(-2\) | \(3\) | \(2\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+2q^{7}+\cdots\) | |
6026.2.a.d | \(1\) | \(48.118\) | \(\Q\) | None | \(1\) | \(2\) | \(-1\) | \(2\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+2q^{7}+\cdots\) | |
6026.2.a.e | \(2\) | \(48.118\) | \(\Q(\sqrt{3}) \) | None | \(2\) | \(2\) | \(0\) | \(4\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\beta )q^{6}+\cdots\) | |
6026.2.a.f | \(20\) | \(48.118\) | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(20\) | \(-5\) | \(-6\) | \(-12\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{3}q^{5}-\beta _{1}q^{6}+\cdots\) | |
6026.2.a.g | \(21\) | \(48.118\) | None | \(21\) | \(0\) | \(-13\) | \(-18\) | \(-\) | \(+\) | \(-\) | |||
6026.2.a.h | \(24\) | \(48.118\) | None | \(-24\) | \(-1\) | \(-1\) | \(-7\) | \(+\) | \(+\) | \(+\) | |||
6026.2.a.i | \(25\) | \(48.118\) | None | \(-25\) | \(-4\) | \(-3\) | \(-11\) | \(+\) | \(-\) | \(-\) | |||
6026.2.a.j | \(33\) | \(48.118\) | None | \(-33\) | \(3\) | \(-4\) | \(11\) | \(+\) | \(-\) | \(+\) | |||
6026.2.a.k | \(35\) | \(48.118\) | None | \(35\) | \(-3\) | \(10\) | \(14\) | \(-\) | \(+\) | \(+\) | |||
6026.2.a.l | \(36\) | \(48.118\) | None | \(-36\) | \(4\) | \(1\) | \(13\) | \(+\) | \(+\) | \(-\) | |||
6026.2.a.m | \(41\) | \(48.118\) | None | \(41\) | \(4\) | \(9\) | \(12\) | \(-\) | \(-\) | \(-\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6026))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(262))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3013))\)\(^{\oplus 2}\)