Defining parameters
Level: | \( N \) | = | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | = | \( 2 \) |
Character orbit: | \([\chi]\) | = | 6036.a (trivial) |
Character field: | \(\Q\) | ||
Newforms: | \( 9 \) | ||
Sturm bound: | \(2016\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6036))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1014 | 84 | 930 |
Cusp forms | 1003 | 84 | 919 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(503\) | Fricke | Dim. |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(26\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(16\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(16\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(26\) |
Plus space | \(+\) | \(32\) | ||
Minus space | \(-\) | \(52\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6036))\) into irreducible Hecke orbits
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 503 | |||||||
6036.2.a.a | \(1\) | \(48.198\) | \(\Q\) | None | \(0\) | \(-1\) | \(-3\) | \(3\) | \(-\) | \(+\) | \(-\) | \(q-q^{3}-3q^{5}+3q^{7}+q^{9}+6q^{11}+\cdots\) | |
6036.2.a.b | \(1\) | \(48.198\) | \(\Q\) | None | \(0\) | \(-1\) | \(3\) | \(1\) | \(-\) | \(+\) | \(-\) | \(q-q^{3}+3q^{5}+q^{7}+q^{9}-2q^{11}-5q^{13}+\cdots\) | |
6036.2.a.c | \(1\) | \(48.198\) | \(\Q\) | None | \(0\) | \(1\) | \(-3\) | \(-5\) | \(-\) | \(-\) | \(-\) | \(q+q^{3}-3q^{5}-5q^{7}+q^{9}-6q^{11}+\cdots\) | |
6036.2.a.d | \(1\) | \(48.198\) | \(\Q\) | None | \(0\) | \(1\) | \(-1\) | \(1\) | \(-\) | \(-\) | \(-\) | \(q+q^{3}-q^{5}+q^{7}+q^{9}+6q^{11}+3q^{13}+\cdots\) | |
6036.2.a.e | \(1\) | \(48.198\) | \(\Q\) | None | \(0\) | \(1\) | \(1\) | \(1\) | \(-\) | \(-\) | \(+\) | \(q+q^{3}+q^{5}+q^{7}+q^{9}-2q^{11}+3q^{13}+\cdots\) | |
6036.2.a.f | \(14\) | \(48.198\) | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) | None | \(0\) | \(-14\) | \(-6\) | \(-7\) | \(-\) | \(+\) | \(-\) | \(q-q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+\beta _{3}q^{11}+\cdots\) | |
6036.2.a.g | \(15\) | \(48.198\) | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) | None | \(0\) | \(15\) | \(-11\) | \(-4\) | \(-\) | \(-\) | \(+\) | \(q+q^{3}+(-1+\beta _{1})q^{5}-\beta _{8}q^{7}+q^{9}+\cdots\) | |
6036.2.a.h | \(24\) | \(48.198\) | None | \(0\) | \(24\) | \(18\) | \(9\) | \(-\) | \(-\) | \(-\) | |||
6036.2.a.i | \(26\) | \(48.198\) | None | \(0\) | \(-26\) | \(6\) | \(5\) | \(-\) | \(+\) | \(+\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6036))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6036)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1509))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3018))\)\(^{\oplus 2}\)