Properties

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

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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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
2880.2.a.a 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
2880.2.a.b 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+6q^{13}+2q^{17}+4q^{19}+\cdots\)
2880.2.a.c 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
2880.2.a.d 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
2880.2.a.e 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-2q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.f 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-2q^{13}+6q^{17}-4q^{19}+\cdots\)
2880.2.a.g 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots\)
2880.2.a.h 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+6q^{11}+4q^{13}-6q^{17}+\cdots\)
2880.2.a.i 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}-2q^{13}+2q^{17}+8q^{19}+\cdots\)
2880.2.a.j 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}-2q^{13}+2q^{17}-8q^{19}+\cdots\)
2880.2.a.k 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-6q^{11}+4q^{13}-6q^{17}+\cdots\)
2880.2.a.l 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots\)
2880.2.a.m 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{13}+6q^{17}+4q^{19}+\cdots\)
2880.2.a.n 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+2q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.o 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots\)
2880.2.a.p 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
2880.2.a.q 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-2q^{13}-6q^{17}-4q^{19}+\cdots\)
2880.2.a.r 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
2880.2.a.s 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}+2q^{13}+6q^{17}+4q^{23}+\cdots\)
2880.2.a.t 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
2880.2.a.u 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-6q^{11}+4q^{13}+6q^{17}+\cdots\)
2880.2.a.v 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots\)
2880.2.a.w 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+2q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.x 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}-6q^{13}+6q^{17}+4q^{19}+\cdots\)
2880.2.a.y 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
2880.2.a.z 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{13}-6q^{17}-4q^{19}+8q^{23}+\cdots\)
2880.2.a.ba 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{13}-6q^{17}+4q^{19}-8q^{23}+\cdots\)
2880.2.a.bb 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}-6q^{13}+6q^{17}-4q^{19}+\cdots\)
2880.2.a.bc 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2880.2.a.bd 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-2q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.be 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots\)
2880.2.a.bf 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+6q^{11}+4q^{13}+6q^{17}+\cdots\)
2880.2.a.bg 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-4q^{11}+2q^{13}-2q^{17}+\cdots\)
2880.2.a.bh 2880.a 1.a $1$ $22.997$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+2q^{13}+6q^{17}-4q^{23}+\cdots\)
2880.2.a.bi 2880.a 1.a $2$ $22.997$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}-\beta q^{11}-4q^{13}+2q^{17}+\cdots\)
2880.2.a.bj 2880.a 1.a $2$ $22.997$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+\beta q^{11}-4q^{13}-2q^{17}+\cdots\)
2880.2.a.bk 2880.a 1.a $2$ $22.997$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+2\beta q^{11}+2q^{13}-2q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2880))\) into lower level spaces

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