Defining parameters
Level: | \( N \) | \(=\) | \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2898.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 35 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2898))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 592 | 56 | 536 |
Cusp forms | 561 | 56 | 505 |
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.
\(2\) | \(3\) | \(7\) | \(23\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(5\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(1\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(5\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(4\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(1\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(22\) | |||
Minus space | \(-\) | \(34\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2898))\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 7 | 23 | |||||||
2898.2.a.a | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(-3\) | \(-1\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}-3q^{5}-q^{7}-q^{8}+3q^{10}+\cdots\) | |
2898.2.a.b | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(-3\) | \(1\) | \(+\) | \(+\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\) | |
2898.2.a.c | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(-1\) | \(-1\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\) | |
2898.2.a.d | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(-1\) | \(1\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}-q^{5}+q^{7}-q^{8}+q^{10}+\cdots\) | |
2898.2.a.e | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(1\) | \(+\) | \(+\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}+q^{5}+q^{7}-q^{8}-q^{10}+\cdots\) | |
2898.2.a.f | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(-1\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\) | |
2898.2.a.g | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(-1\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\) | |
2898.2.a.h | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(1\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\) | |
2898.2.a.i | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(2\) | \(1\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}+2q^{5}+q^{7}-q^{8}-2q^{10}+\cdots\) | |
2898.2.a.j | \(1\) | \(23.141\) | \(\Q\) | None | \(-1\) | \(0\) | \(3\) | \(1\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\) | |
2898.2.a.k | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(-3\) | \(1\) | \(-\) | \(-\) | \(-\) | \(-\) | \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\) | |
2898.2.a.l | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(-2\) | \(1\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}-2q^{5}+q^{7}+q^{8}-2q^{10}+\cdots\) | |
2898.2.a.m | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(-1\) | \(1\) | \(-\) | \(+\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\) | |
2898.2.a.n | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(0\) | \(-1\) | \(-\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots\) | |
2898.2.a.o | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\) | |
2898.2.a.p | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(-\) | \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+q^{14}+\cdots\) | |
2898.2.a.q | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(1\) | \(-1\) | \(-\) | \(+\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\) | |
2898.2.a.r | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(2\) | \(-1\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}+2q^{10}+\cdots\) | |
2898.2.a.s | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(2\) | \(1\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\) | |
2898.2.a.t | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(3\) | \(1\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\) | |
2898.2.a.u | \(1\) | \(23.141\) | \(\Q\) | None | \(1\) | \(0\) | \(4\) | \(1\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}+4q^{5}+q^{7}+q^{8}+4q^{10}+\cdots\) | |
2898.2.a.v | \(2\) | \(23.141\) | \(\Q(\sqrt{5}) \) | None | \(-2\) | \(0\) | \(-4\) | \(2\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}+2q^{10}+\cdots\) | |
2898.2.a.w | \(2\) | \(23.141\) | \(\Q(\sqrt{3}) \) | None | \(-2\) | \(0\) | \(-2\) | \(2\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}+(-1+\beta )q^{5}+q^{7}-q^{8}+\cdots\) | |
2898.2.a.x | \(2\) | \(23.141\) | \(\Q(\sqrt{33}) \) | None | \(-2\) | \(0\) | \(3\) | \(-2\) | \(+\) | \(-\) | \(+\) | \(-\) | \(q-q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}-q^{8}+\cdots\) | |
2898.2.a.y | \(2\) | \(23.141\) | \(\Q(\sqrt{2}) \) | None | \(-2\) | \(0\) | \(4\) | \(-2\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{7}-q^{8}+\cdots\) | |
2898.2.a.z | \(2\) | \(23.141\) | \(\Q(\sqrt{2}) \) | None | \(2\) | \(0\) | \(-4\) | \(-2\) | \(-\) | \(+\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}+(-2+\beta )q^{5}-q^{7}+q^{8}+\cdots\) | |
2898.2.a.ba | \(2\) | \(23.141\) | \(\Q(\sqrt{17}) \) | None | \(2\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+q^{4}-\beta q^{5}-q^{7}+q^{8}-\beta q^{10}+\cdots\) | |
2898.2.a.bb | \(2\) | \(23.141\) | \(\Q(\sqrt{41}) \) | None | \(2\) | \(0\) | \(-1\) | \(2\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{4}-\beta q^{5}+q^{7}+q^{8}-\beta q^{10}+\cdots\) | |
2898.2.a.bc | \(2\) | \(23.141\) | \(\Q(\sqrt{41}) \) | None | \(2\) | \(0\) | \(1\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\) | |
2898.2.a.bd | \(2\) | \(23.141\) | \(\Q(\sqrt{5}) \) | None | \(2\) | \(0\) | \(2\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\) | |
2898.2.a.be | \(3\) | \(23.141\) | 3.3.316.1 | None | \(-3\) | \(0\) | \(-4\) | \(-3\) | \(+\) | \(-\) | \(+\) | \(-\) | \(q-q^{2}+q^{4}+(-1+\beta _{2})q^{5}-q^{7}-q^{8}+\cdots\) | |
2898.2.a.bf | \(3\) | \(23.141\) | 3.3.568.1 | None | \(-3\) | \(0\) | \(-1\) | \(-3\) | \(+\) | \(+\) | \(+\) | \(-\) | \(q-q^{2}+q^{4}+\beta _{2}q^{5}-q^{7}-q^{8}-\beta _{2}q^{10}+\cdots\) | |
2898.2.a.bg | \(3\) | \(23.141\) | 3.3.568.1 | None | \(3\) | \(0\) | \(1\) | \(-3\) | \(-\) | \(+\) | \(+\) | \(+\) | \(q+q^{2}+q^{4}-\beta _{2}q^{5}-q^{7}+q^{8}-\beta _{2}q^{10}+\cdots\) | |
2898.2.a.bh | \(4\) | \(23.141\) | 4.4.271296.1 | None | \(-4\) | \(0\) | \(0\) | \(4\) | \(+\) | \(+\) | \(-\) | \(+\) | \(q-q^{2}+q^{4}+\beta _{1}q^{5}+q^{7}-q^{8}-\beta _{1}q^{10}+\cdots\) | |
2898.2.a.bi | \(4\) | \(23.141\) | 4.4.271296.1 | None | \(4\) | \(0\) | \(0\) | \(4\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}+q^{4}-\beta _{1}q^{5}+q^{7}+q^{8}-\beta _{1}q^{10}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2898))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2898)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(414))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(483))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(966))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1449))\)\(^{\oplus 2}\)