Defining parameters
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 13 \) | ||
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 newform subspaces
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
\( S_{2}^{\mathrm{old}}(\Gamma_0(6026)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(131))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(262))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3013))\)\(^{\oplus 2}\)