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

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