Defining parameters
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 37 \) | ||
Sturm bound: | \(1152\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2880))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 624 | 40 | 584 |
Cusp forms | 529 | 40 | 489 |
Eisenstein series | 95 | 0 | 95 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(4\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(7\) |
Plus space | \(+\) | \(18\) | ||
Minus space | \(-\) | \(22\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\) 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 | |||||||
2880.2.a.a | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-4\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}-4q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\) | |
2880.2.a.b | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-4\) | \(-\) | \(-\) | \(+\) | \(q-q^{5}-4q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\) | |
2880.2.a.c | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-4\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}-4q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\) | |
2880.2.a.d | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}-2q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\) | |
2880.2.a.e | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(+\) | \(+\) | \(q-q^{5}-2q^{7}-2q^{11}-4q^{13}+2q^{17}+\cdots\) | |
2880.2.a.f | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(q-q^{5}-2q^{7}-2q^{13}+6q^{17}-4q^{19}+\cdots\) | |
2880.2.a.g | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | \(+\) | \(+\) | \(+\) | \(q-q^{5}-2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots\) | |
2880.2.a.h | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(-2\) | \(-\) | \(+\) | \(+\) | \(q-q^{5}-2q^{7}+6q^{11}+4q^{13}-6q^{17}+\cdots\) | |
2880.2.a.i | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | \(-\) | \(-\) | \(+\) | \(q-q^{5}-4q^{11}-2q^{13}+2q^{17}+8q^{19}+\cdots\) | |
2880.2.a.j | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(0\) | \(-\) | \(-\) | \(+\) | \(q-q^{5}+4q^{11}-2q^{13}+2q^{17}-8q^{19}+\cdots\) | |
2880.2.a.k | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(2\) | \(+\) | \(+\) | \(+\) | \(q-q^{5}+2q^{7}-6q^{11}+4q^{13}-6q^{17}+\cdots\) | |
2880.2.a.l | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(2\) | \(+\) | \(+\) | \(+\) | \(q-q^{5}+2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots\) | |
2880.2.a.m | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(2\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}+2q^{7}-2q^{13}+6q^{17}+4q^{19}+\cdots\) | |
2880.2.a.n | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(2\) | \(+\) | \(+\) | \(+\) | \(q-q^{5}+2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots\) | |
2880.2.a.o | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(2\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}+2q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots\) | |
2880.2.a.p | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(4\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}+4q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\) | |
2880.2.a.q | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(4\) | \(-\) | \(-\) | \(+\) | \(q-q^{5}+4q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\) | |
2880.2.a.r | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(-1\) | \(4\) | \(+\) | \(-\) | \(+\) | \(q-q^{5}+4q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\) | |
2880.2.a.s | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-4\) | \(-\) | \(-\) | \(-\) | \(q+q^{5}-4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots\) | |
2880.2.a.t | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-4\) | \(+\) | \(-\) | \(-\) | \(q+q^{5}-4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\) | |
2880.2.a.u | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-2\) | \(-\) | \(+\) | \(-\) | \(q+q^{5}-2q^{7}-6q^{11}+4q^{13}+6q^{17}+\cdots\) | |
2880.2.a.v | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-2\) | \(+\) | \(+\) | \(-\) | \(q+q^{5}-2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots\) | |
2880.2.a.w | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(-2\) | \(-\) | \(+\) | \(-\) | \(q+q^{5}-2q^{7}+2q^{11}-4q^{13}-2q^{17}+\cdots\) | |
2880.2.a.x | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(+\) | \(-\) | \(-\) | \(q+q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots\) | |
2880.2.a.y | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(+\) | \(-\) | \(-\) | \(q+q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\) | |
2880.2.a.z | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(+\) | \(-\) | \(-\) | \(q+q^{5}-2q^{13}-6q^{17}-4q^{19}+8q^{23}+\cdots\) | |
2880.2.a.ba | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(+\) | \(-\) | \(-\) | \(q+q^{5}-2q^{13}-6q^{17}+4q^{19}-8q^{23}+\cdots\) | |
2880.2.a.bb | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(-\) | \(-\) | \(-\) | \(q+q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots\) | |
2880.2.a.bc | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(0\) | \(-\) | \(-\) | \(-\) | \(q+q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\) | |
2880.2.a.bd | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(2\) | \(+\) | \(+\) | \(-\) | \(q+q^{5}+2q^{7}-2q^{11}-4q^{13}-2q^{17}+\cdots\) | |
2880.2.a.be | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(2\) | \(+\) | \(+\) | \(-\) | \(q+q^{5}+2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots\) | |
2880.2.a.bf | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(2\) | \(+\) | \(+\) | \(-\) | \(q+q^{5}+2q^{7}+6q^{11}+4q^{13}+6q^{17}+\cdots\) | |
2880.2.a.bg | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(4\) | \(-\) | \(-\) | \(-\) | \(q+q^{5}+4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\) | |
2880.2.a.bh | \(1\) | \(22.997\) | \(\Q\) | None | \(0\) | \(0\) | \(1\) | \(4\) | \(-\) | \(-\) | \(-\) | \(q+q^{5}+4q^{7}+2q^{13}+6q^{17}-4q^{23}+\cdots\) | |
2880.2.a.bi | \(2\) | \(22.997\) | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(-\) | \(+\) | \(+\) | \(q-q^{5}-\beta q^{7}-\beta q^{11}-4q^{13}+2q^{17}+\cdots\) | |
2880.2.a.bj | \(2\) | \(22.997\) | \(\Q(\sqrt{5}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(-\) | \(+\) | \(-\) | \(q+q^{5}-\beta q^{7}+\beta q^{11}-4q^{13}-2q^{17}+\cdots\) | |
2880.2.a.bk | \(2\) | \(22.997\) | \(\Q(\sqrt{2}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(-\) | \(-\) | \(-\) | \(q+q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}-2q^{17}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2880))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 2}\)