Space of modular forms of level 2880, weight 3, and Character 2880.e

• Label: 2880.3.e
• Level: $2880$
• Weight: $3$
• Character orbit: 2880.e
• Rep. character: $\chi_{2880}(2431,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $14$
• Sturm bound: $1728$
• Trace bound: $37$

Defining parameters

Level:	$N$	$=$	$2880 = 2^{6} \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	2880.e (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$4$
Character field:			$\Q$
Newform subspaces:			$14$
Sturm bound:			$1728$
Trace bound:			$37$
Distinguishing $T_p$:			$7$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{3}(2880, [\chi])$.

	Total	New	Old
Modular forms	1200	80	1120
Cusp forms	1104	80	1024
Eisenstein series	96	0	96

Trace form

$80 q + 32 q^{13} + 400 q^{25} + 32 q^{29} + 64 q^{37} - 96 q^{41} - 560 q^{49} + 160 q^{53} - 256 q^{61} - 224 q^{77} - 160 q^{85} - 96 q^{89}+O(q^{100})$

Decomposition of $S_{3}^{\mathrm{new}}(2880, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2880.3.e.a	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(i, \sqrt{5})$	None					160.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+(\beta _{1}-4\beta _{2})q^{7}+(-3\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots$
2880.3.e.b	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(\sqrt{-3}, \sqrt{5})$	None					80.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}+2\beta _{3}q^{11}+(-4+\cdots)q^{13}+\cdots$
2880.3.e.c	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(\sqrt{-3}, \sqrt{5})$	None					720.3.e.d	$4$	$0$	$0$	$0$	$0$	$0$	$2^{6}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}-4q^{13}+\cdots$
2880.3.e.d	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(\sqrt{-3}, \sqrt{5})$	None					240.3.e.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{2}q^{11}+(-4+6\beta _{1}+\cdots)q^{13}+\cdots$
2880.3.e.e	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(\zeta_{10})$	None					20.3.b.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta_{2} q^{5}+(-\beta_{3}-\beta_1)q^{7}+(2\beta_{3}-2\beta_1)q^{11}+\cdots$
2880.3.e.f	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(\sqrt{-3}, \sqrt{5})$	None					240.3.e.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}+(\beta _{2}-\beta _{3})q^{11}+(8+\cdots)q^{13}+\cdots$
2880.3.e.g	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(\sqrt{-3}, \sqrt{5})$	None					720.3.e.b	$4$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+8q^{13}+\cdots$
2880.3.e.h	$2880$	$3$	2880.e	4.b	$2$	$4$	$4$	$78.474$	$\Q(i, \sqrt{5})$	None					160.3.b.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{5}+\beta _{1}q^{7}+(5\beta _{1}+\beta _{3})q^{11}+\cdots$
2880.3.e.i	$2880$	$3$	2880.e	4.b	$2$	$8$	$8$	$78.474$	8.0.$\cdots$.1	None					180.3.c.c	$4$	$0$	$0$	$0$	$0$	$0$	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{5}q^{7}-\beta _{4}q^{11}+(-2-\beta _{7})q^{13}+\cdots$
2880.3.e.j	$2880$	$3$	2880.e	4.b	$2$	$8$	$8$	$78.474$	8.0.85100625.1	None					60.3.c.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{19}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+(-\beta _{1}+\beta _{7})q^{11}+\cdots$
2880.3.e.k	$2880$	$3$	2880.e	4.b	$2$	$8$	$8$	$78.474$	8.0.12960000.1	None					480.3.e.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}+(\beta _{2}+\beta _{4})q^{7}+(-\beta _{4}-\beta _{5}+\cdots)q^{11}+\cdots$
2880.3.e.l	$2880$	$3$	2880.e	4.b	$2$	$8$	$8$	$78.474$	8.0.3364000000.3	None					1440.3.e.c	$2$	$0$	$0$	$0$	$0$	$0$	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{5}-\beta _{6}q^{7}+(\beta _{2}-2\beta _{5}-\beta _{6}+\cdots)q^{11}+\cdots$
2880.3.e.m	$2880$	$3$	2880.e	4.b	$2$	$8$	$8$	$78.474$	8.0.3364000000.3	None					1440.3.e.c	$2$	$0$	$0$	$0$	$0$	$0$	$2^{17}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}-\beta _{6}q^{7}+(-\beta _{2}+2\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots$
2880.3.e.n	$2880$	$3$	2880.e	4.b	$2$	$8$	$8$	$78.474$	8.0.12960000.1	None					480.3.e.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{5}+(\beta _{2}+\beta _{4}-\beta _{6})q^{7}+(-2\beta _{2}+\cdots)q^{11}+\cdots$

Decomposition of $S_{3}^{\mathrm{old}}(2880, [\chi])$ into lower level spaces

$S_{3}^{\mathrm{old}}(2880, [\chi]) \simeq$ $S_{3}^{\mathrm{new}}(12, [\chi])$$^{\oplus 20}$$\oplus$$S_{3}^{\mathrm{new}}(16, [\chi])$$^{\oplus 18}$$\oplus$$S_{3}^{\mathrm{new}}(20, [\chi])$$^{\oplus 15}$$\oplus$$S_{3}^{\mathrm{new}}(32, [\chi])$$^{\oplus 12}$$\oplus$$S_{3}^{\mathrm{new}}(36, [\chi])$$^{\oplus 10}$$\oplus$$S_{3}^{\mathrm{new}}(48, [\chi])$$^{\oplus 12}$$\oplus$$S_{3}^{\mathrm{new}}(60, [\chi])$$^{\oplus 10}$$\oplus$$S_{3}^{\mathrm{new}}(64, [\chi])$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(80, [\chi])$$^{\oplus 9}$$\oplus$$S_{3}^{\mathrm{new}}(96, [\chi])$$^{\oplus 8}$$\oplus$$S_{3}^{\mathrm{new}}(144, [\chi])$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(160, [\chi])$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(180, [\chi])$$^{\oplus 5}$$\oplus$$S_{3}^{\mathrm{new}}(192, [\chi])$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(240, [\chi])$$^{\oplus 6}$$\oplus$$S_{3}^{\mathrm{new}}(288, [\chi])$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(320, [\chi])$$^{\oplus 3}$$\oplus$$S_{3}^{\mathrm{new}}(480, [\chi])$$^{\oplus 4}$$\oplus$$S_{3}^{\mathrm{new}}(576, [\chi])$$^{\oplus 2}$$\oplus$$S_{3}^{\mathrm{new}}(720, [\chi])$$^{\oplus 3}$$\oplus$$S_{3}^{\mathrm{new}}(960, [\chi])$$^{\oplus 2}$$\oplus$$S_{3}^{\mathrm{new}}(1440, [\chi])$$^{\oplus 2}$