Defining parameters
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(1806\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6010))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 906 | 199 | 707 |
Cusp forms | 899 | 199 | 700 |
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.
\(2\) | \(5\) | \(601\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(29\) |
\(+\) | \(+\) | \(-\) | $-$ | \(21\) |
\(+\) | \(-\) | \(+\) | $-$ | \(27\) |
\(+\) | \(-\) | \(-\) | $+$ | \(23\) |
\(-\) | \(+\) | \(+\) | $-$ | \(28\) |
\(-\) | \(+\) | \(-\) | $+$ | \(22\) |
\(-\) | \(-\) | \(+\) | $+$ | \(16\) |
\(-\) | \(-\) | \(-\) | $-$ | \(33\) |
Plus space | \(+\) | \(90\) | ||
Minus space | \(-\) | \(109\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6010))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 5 | 601 | |||||||
6010.2.a.a | $1$ | $47.990$ | \(\Q\) | None | \(-1\) | \(-3\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots\) | |
6010.2.a.b | $1$ | $47.990$ | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(0\) | $+$ | $-$ | $-$ | \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\) | |
6010.2.a.c | $16$ | $47.990$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(16\) | \(-8\) | \(16\) | \(-10\) | $-$ | $-$ | $+$ | \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\) | |
6010.2.a.d | $21$ | $47.990$ | None | \(-21\) | \(-1\) | \(21\) | \(0\) | $+$ | $-$ | $-$ | |||
6010.2.a.e | $21$ | $47.990$ | None | \(-21\) | \(8\) | \(-21\) | \(0\) | $+$ | $+$ | $-$ | |||
6010.2.a.f | $22$ | $47.990$ | None | \(22\) | \(-6\) | \(-22\) | \(-12\) | $-$ | $+$ | $-$ | |||
6010.2.a.g | $27$ | $47.990$ | None | \(-27\) | \(6\) | \(27\) | \(0\) | $+$ | $-$ | $+$ | |||
6010.2.a.h | $28$ | $47.990$ | None | \(28\) | \(4\) | \(-28\) | \(10\) | $-$ | $+$ | $+$ | |||
6010.2.a.i | $29$ | $47.990$ | None | \(-29\) | \(-10\) | \(-29\) | \(0\) | $+$ | $+$ | $+$ | |||
6010.2.a.j | $33$ | $47.990$ | None | \(33\) | \(6\) | \(33\) | \(4\) | $-$ | $-$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6010))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6010)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(601))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1202))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3005))\)\(^{\oplus 2}\)