Space of modular forms of level 2240, weight 2, and Character 2240.g

• Label: 2240.2.g
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.g
• Rep. character: $\chi_{2240}(449,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $16$
• Sturm bound: $768$
• Trace bound: $19$

Defining parameters

Level:	$N$	$=$	$2240 = 2^{6} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2240.g (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$16$
Sturm bound:			$768$
Trace bound:			$19$
Distinguishing $T_p$:			$3$, $11$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(2240, [\chi])$.

	Total	New	Old
Modular forms	408	72	336
Cusp forms	360	72	288
Eisenstein series	48	0	48

Trace form

$72 q - 72 q^{9} - 8 q^{25} + 16 q^{41} - 48 q^{45} - 72 q^{49} - 32 q^{61} - 16 q^{65} + 128 q^{69} + 72 q^{81} + 16 q^{89}+O(q^{100})$

Decomposition of $S_{2}^{\mathrm{new}}(2240, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2240.2.g.a	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					280.2.g.a	$2$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(i-2)q^{5}-i q^{7}+2 q^{9}+\cdots$
2240.2.g.b	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					280.2.g.a	$2$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-i-2)q^{5}-i q^{7}+2 q^{9}+\cdots$
2240.2.g.c	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					140.2.e.b	$2$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2 i-1)q^{5}+i q^{7}+3 q^{9}-4 i q^{13}+\cdots$
2240.2.g.d	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					140.2.e.b	$2$	$0$	$0$	$0$	$-2$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2 i-1)q^{5}-i q^{7}+3 q^{9}-4 i q^{13}+\cdots$
2240.2.g.e	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					140.2.e.a	$2$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(i+2)q^{5}+i q^{7}-6 q^{9}+\cdots$
2240.2.g.f	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					140.2.e.a	$2$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3 i q^{3}+(-i+2)q^{5}+i q^{7}-6 q^{9}+\cdots$
2240.2.g.g	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					35.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(-i+2)q^{5}-i q^{7}+2 q^{9}+\cdots$
2240.2.g.h	$2240$	$2$	2240.g	5.b	$2$	$2$	$2$	$17.886$	$\Q(\sqrt{-1})$	None					35.2.b.a	$2$	$0$	$0$	$0$	$4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+i q^{3}+(i+2)q^{5}-i q^{7}+2 q^{9}+\cdots$
2240.2.g.i	$2240$	$2$	2240.g	5.b	$2$	$4$	$4$	$17.886$	$\Q(i, \sqrt{6})$	None					70.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+\cdots$
2240.2.g.j	$2240$	$2$	2240.g	5.b	$2$	$4$	$4$	$17.886$	$\Q(i, \sqrt{6})$	None					70.2.c.a	$2$	$0$	$0$	$0$	$-4$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{3})q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots$
2240.2.g.k	$2240$	$2$	2240.g	5.b	$2$	$4$	$4$	$17.886$	$\Q(i, \sqrt{5})$	None					1120.2.g.a	$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{1}q^{7}+2q^{9}+\beta _{3}q^{11}+\cdots$
2240.2.g.l	$2240$	$2$	2240.g	5.b	$2$	$6$	$6$	$17.886$	6.0.5161984.1	None					280.2.g.b	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(-\beta _{2}-\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots$
2240.2.g.m	$2240$	$2$	2240.g	5.b	$2$	$6$	$6$	$17.886$	6.0.5161984.1	None					280.2.g.b	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(-\beta _{1}+\beta _{5})q^{5}-\beta _{4}q^{7}+\cdots$
2240.2.g.n	$2240$	$2$	2240.g	5.b	$2$	$10$	$10$	$17.886$	10.0.$\cdots$.1	None					1120.2.g.b	$2$	$0$	$0$	$0$	$2$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{4}q^{5}-\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
2240.2.g.o	$2240$	$2$	2240.g	5.b	$2$	$10$	$10$	$17.886$	10.0.$\cdots$.1	None					1120.2.g.b	$2$	$0$	$0$	$0$	$2$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{6}q^{5}-\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$
2240.2.g.p	$2240$	$2$	2240.g	5.b	$2$	$12$	$12$	$17.886$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None			✓		1120.2.g.d	$4$	$0$	$0$	$0$	$0$	$0$	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{9}q^{3}-\beta _{10}q^{5}-\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(2240, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(2240, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(35, [\chi])$$^{\oplus 7}$$\oplus$$S_{2}^{\mathrm{new}}(40, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(70, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(80, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(140, [\chi])$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(160, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(280, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(320, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(560, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1120, [\chi])$$^{\oplus 2}$