Defining parameters
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(570))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 128 | 13 | 115 |
Cusp forms | 113 | 13 | 100 |
Eisenstein series | 15 | 0 | 15 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(19\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(1\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(1\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(2\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(2\) |
Plus space | \(+\) | \(3\) | |||
Minus space | \(-\) | \(10\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(570))\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 5 | 19 | |||||||
570.2.a.a | \(1\) | \(4.551\) | \(\Q\) | None | \(-1\) | \(-1\) | \(-1\) | \(-2\) | \(+\) | \(+\) | \(+\) | \(-\) | \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-2q^{7}+\cdots\) | |
570.2.a.b | \(1\) | \(4.551\) | \(\Q\) | None | \(-1\) | \(-1\) | \(-1\) | \(2\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\) | |
570.2.a.c | \(1\) | \(4.551\) | \(\Q\) | None | \(-1\) | \(-1\) | \(1\) | \(-2\) | \(+\) | \(+\) | \(-\) | \(-\) | \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\) | |
570.2.a.d | \(1\) | \(4.551\) | \(\Q\) | None | \(-1\) | \(1\) | \(-1\) | \(4\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\) | |
570.2.a.e | \(1\) | \(4.551\) | \(\Q\) | None | \(-1\) | \(1\) | \(1\) | \(-4\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\) | |
570.2.a.f | \(1\) | \(4.551\) | \(\Q\) | None | \(-1\) | \(1\) | \(1\) | \(2\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\) | |
570.2.a.g | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(-1\) | \(-1\) | \(0\) | \(-\) | \(+\) | \(+\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\) | |
570.2.a.h | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(-1\) | \(1\) | \(-2\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\) | |
570.2.a.i | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(-1\) | \(1\) | \(4\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots\) | |
570.2.a.j | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(1\) | \(-1\) | \(2\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\) | |
570.2.a.k | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(1\) | \(-1\) | \(2\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\) | |
570.2.a.l | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(1\) | \(1\) | \(-2\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\) | |
570.2.a.m | \(1\) | \(4.551\) | \(\Q\) | None | \(1\) | \(1\) | \(1\) | \(4\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(570))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(570)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)