Properties

Label 2880.2.a
Level 2880
Weight 2
Character orbit a
Rep. character \(\chi_{2880}(1,\cdot)\)
Character field \(\Q\)
Dimension 40
Newform subspaces 37
Sturm bound 1152
Trace bound 19

Related objects

Downloads

Learn more about

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.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(7\)
Plus space\(+\)\(18\)
Minus space\(-\)\(22\)

Trace form

\( 40q + O(q^{10}) \) \( 40q - 16q^{13} + 40q^{25} - 16q^{29} - 32q^{37} + 16q^{41} + 40q^{49} - 16q^{53} - 16q^{77} + 16q^{85} + 16q^{89} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(\Gamma_0(2880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 2}\)