Defining parameters
Level: | \( N \) | \(=\) | \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1530.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(648\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1530))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 340 | 24 | 316 |
Cusp forms | 309 | 24 | 285 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(17\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(1\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(3\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(3\) |
Plus space | \(+\) | \(9\) | |||
Minus space | \(-\) | \(15\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1530))\) 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 | 17 | |||||||
1530.2.a.a | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(-1\) | \(-4\) | \(+\) | \(+\) | \(+\) | \(-\) | \(q-q^{2}+q^{4}-q^{5}-4q^{7}-q^{8}+q^{10}+\cdots\) | |
1530.2.a.b | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(-1\) | \(0\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\) | |
1530.2.a.c | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(-1\) | \(2\) | \(+\) | \(-\) | \(+\) | \(-\) | \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\) | |
1530.2.a.d | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(-4\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}+q^{5}-4q^{7}-q^{8}-q^{10}+\cdots\) | |
1530.2.a.e | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(-2\) | \(+\) | \(+\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}+q^{5}-2q^{7}-q^{8}-q^{10}+\cdots\) | |
1530.2.a.f | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(0\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-4q^{11}+\cdots\) | |
1530.2.a.g | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(2\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\) | |
1530.2.a.h | \(1\) | \(12.217\) | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(2\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\) | |
1530.2.a.i | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\) | |
1530.2.a.j | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\) | |
1530.2.a.k | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(+\) | \(+\) | \(+\) | \(q+q^{2}+q^{4}-q^{5}-2q^{7}+q^{8}-q^{10}+\cdots\) | |
1530.2.a.l | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(2\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\) | |
1530.2.a.m | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(-4\) | \(-\) | \(+\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\) | |
1530.2.a.n | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(2\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\) | |
1530.2.a.o | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(2\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\) | |
1530.2.a.p | \(1\) | \(12.217\) | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(2\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+q^{5}+2q^{7}+q^{8}+q^{10}+\cdots\) | |
1530.2.a.q | \(2\) | \(12.217\) | \(\Q(\sqrt{5}) \) | None | \(-2\) | \(0\) | \(-2\) | \(2\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}-q^{5}+(1+\beta )q^{7}-q^{8}+\cdots\) | |
1530.2.a.r | \(2\) | \(12.217\) | \(\Q(\sqrt{17}) \) | None | \(-2\) | \(0\) | \(-2\) | \(2\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}-q^{5}+2\beta q^{7}-q^{8}+q^{10}+\cdots\) | |
1530.2.a.s | \(2\) | \(12.217\) | \(\Q(\sqrt{6}) \) | None | \(2\) | \(0\) | \(-2\) | \(0\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}-q^{5}+\beta q^{7}+q^{8}-q^{10}+\cdots\) | |
1530.2.a.t | \(2\) | \(12.217\) | \(\Q(\sqrt{5}) \) | None | \(2\) | \(0\) | \(2\) | \(2\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}+q^{4}+q^{5}+(1+\beta )q^{7}+q^{8}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1530))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(1530)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(765))\)\(^{\oplus 2}\)