Space of modular forms of level 2240, weight 4, and trivial character

• Label: 2240.4.a
• Level: $2240$
• Weight: $4$
• Character orbit: 2240.a
• Rep. character: $\chi_{2240}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $68$
• Sturm bound: $1536$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2240.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 68 \)
Sturm bound:			\(1536\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2240))\).

	Total	New	Old
Modular forms	1176	144	1032
Cusp forms	1128	144	984
Eisenstein series	48	0	48

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(152\)	\(19\)	\(133\)		\(146\)	\(19\)	\(127\)		\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(-\)	\(-\)		\(146\)	\(17\)	\(129\)		\(140\)	\(17\)	\(123\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(142\)	\(16\)	\(126\)		\(136\)	\(16\)	\(120\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(148\)	\(20\)	\(128\)		\(142\)	\(20\)	\(122\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(142\)	\(17\)	\(125\)		\(136\)	\(17\)	\(119\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(148\)	\(19\)	\(129\)		\(142\)	\(19\)	\(123\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(152\)	\(20\)	\(132\)		\(146\)	\(20\)	\(126\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(146\)	\(16\)	\(130\)		\(140\)	\(16\)	\(124\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(600\)	\(78\)	\(522\)		\(576\)	\(78\)	\(498\)		\(24\)	\(0\)	\(24\)
Minus space			\(-\)		\(576\)	\(66\)	\(510\)		\(552\)	\(66\)	\(486\)		\(24\)	\(0\)	\(24\)

Trace form

\( 144 q + 1296 q^{9} + 3600 q^{25} - 400 q^{29} - 928 q^{33} - 16 q^{37} - 160 q^{41} + 7056 q^{49} + 752 q^{53} + 1376 q^{57} - 1824 q^{61} - 1056 q^{69} + 1904 q^{77} + 15344 q^{81} + 480 q^{85} - 8544 q^{93}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2240))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	5	7
2240.4.a.a	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.f	$1$	$0$	\(0\)	\(-9\)	\(-5\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-9q^{3}-5q^{5}-7q^{7}+54q^{9}-55q^{11}+\cdots\)
2240.4.a.b	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				35.4.a.a	$1$	$0$	\(0\)	\(-8\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}+5q^{5}-7q^{7}+37q^{9}+12q^{11}+\cdots\)
2240.4.a.c	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.e	$1$	$0$	\(0\)	\(-8\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}+5q^{5}+7q^{7}+37q^{9}-28q^{11}+\cdots\)
2240.4.a.d	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.a	$1$	$1$	\(0\)	\(-8\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-8q^{3}+5q^{5}+7q^{7}+37q^{9}+68q^{11}+\cdots\)
2240.4.a.e	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.d	$1$	$1$	\(0\)	\(-7\)	\(-5\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}-5q^{5}+7q^{7}+22q^{9}-9q^{11}+\cdots\)
2240.4.a.f	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.f	$1$	$0$	\(0\)	\(-7\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-7q^{3}+5q^{5}+7q^{7}+22q^{9}+33q^{11}+\cdots\)
2240.4.a.g	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.b	$1$	$1$	\(0\)	\(-5\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}-5q^{5}-7q^{7}-2q^{9}-15q^{11}+\cdots\)
2240.4.a.h	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.e	$1$	$0$	\(0\)	\(-5\)	\(-5\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}-5q^{5}-7q^{7}-2q^{9}+q^{11}+\cdots\)
2240.4.a.i	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.a	$1$	$0$	\(0\)	\(-5\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}+5q^{5}-7q^{7}-2q^{9}+15q^{11}+\cdots\)
2240.4.a.j	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.c	$1$	$1$	\(0\)	\(-5\)	\(5\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-5q^{3}+5q^{5}-7q^{7}-2q^{9}+39q^{11}+\cdots\)
2240.4.a.k	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				1120.4.a.b	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}-7q^{7}-11q^{9}-6^{2}q^{11}+\cdots\)
2240.4.a.l	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.a	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}-7q^{7}-11q^{9}+20q^{11}+\cdots\)
2240.4.a.m	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.d	$1$	$1$	\(0\)	\(-4\)	\(-5\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}+7q^{7}-11q^{9}-60q^{11}+\cdots\)
2240.4.a.n	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.c	$1$	$0$	\(0\)	\(-4\)	\(-5\)	\(7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}-5q^{5}+7q^{7}-11q^{9}+68q^{11}+\cdots\)
2240.4.a.o	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				1120.4.a.a	$1$	$0$	\(0\)	\(-4\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{3}+5q^{5}-7q^{7}-11q^{9}+24q^{11}+\cdots\)
2240.4.a.p	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.b	$1$	$0$	\(0\)	\(-3\)	\(-5\)	\(7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-5q^{5}+7q^{7}-18q^{9}-17q^{11}+\cdots\)
2240.4.a.q	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.b	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-5q^{5}-7q^{7}-26q^{9}-39q^{11}+\cdots\)
2240.4.a.r	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.c	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+5q^{5}-7q^{7}-26q^{9}-65q^{11}+\cdots\)
2240.4.a.s	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.d	$1$	$1$	\(0\)	\(-1\)	\(5\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+5q^{5}-7q^{7}-26q^{9}+7q^{11}+\cdots\)
2240.4.a.t	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.b	$1$	$1$	\(0\)	\(1\)	\(-5\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-5q^{5}+7q^{7}-26q^{9}+39q^{11}+\cdots\)
2240.4.a.u	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.d	$1$	$1$	\(0\)	\(1\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+5q^{5}+7q^{7}-26q^{9}-7q^{11}+\cdots\)
2240.4.a.v	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.c	$1$	$0$	\(0\)	\(1\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+5q^{5}+7q^{7}-26q^{9}+65q^{11}+\cdots\)
2240.4.a.w	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.b	$1$	$0$	\(0\)	\(3\)	\(-5\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-5q^{5}-7q^{7}-18q^{9}+17q^{11}+\cdots\)
2240.4.a.x	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.c	$1$	$0$	\(0\)	\(4\)	\(-5\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-5q^{5}-7q^{7}-11q^{9}-68q^{11}+\cdots\)
2240.4.a.y	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.d	$1$	$1$	\(0\)	\(4\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-5q^{5}-7q^{7}-11q^{9}+60q^{11}+\cdots\)
2240.4.a.z	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.a	$1$	$1$	\(0\)	\(4\)	\(-5\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-5q^{5}+7q^{7}-11q^{9}-20q^{11}+\cdots\)
2240.4.a.ba	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				1120.4.a.b	$1$	$0$	\(0\)	\(4\)	\(-5\)	\(7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}-5q^{5}+7q^{7}-11q^{9}+6^{2}q^{11}+\cdots\)
2240.4.a.bb	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				1120.4.a.a	$1$	$1$	\(0\)	\(4\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{3}+5q^{5}+7q^{7}-11q^{9}-24q^{11}+\cdots\)
2240.4.a.bc	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.e	$1$	$0$	\(0\)	\(5\)	\(-5\)	\(7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}-5q^{5}+7q^{7}-2q^{9}-q^{11}+\cdots\)
2240.4.a.bd	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.b	$1$	$1$	\(0\)	\(5\)	\(-5\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}-5q^{5}+7q^{7}-2q^{9}+15q^{11}+\cdots\)
2240.4.a.be	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.c	$1$	$1$	\(0\)	\(5\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}+5q^{5}+7q^{7}-2q^{9}-39q^{11}+\cdots\)
2240.4.a.bf	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.a	$1$	$0$	\(0\)	\(5\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+5q^{3}+5q^{5}+7q^{7}-2q^{9}-15q^{11}+\cdots\)
2240.4.a.bg	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				280.4.a.d	$1$	$1$	\(0\)	\(7\)	\(-5\)	\(-7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}-5q^{5}-7q^{7}+22q^{9}+9q^{11}+\cdots\)
2240.4.a.bh	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.f	$1$	$0$	\(0\)	\(7\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+7q^{3}+5q^{5}-7q^{7}+22q^{9}-33q^{11}+\cdots\)
2240.4.a.bi	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				70.4.a.a	$1$	$1$	\(0\)	\(8\)	\(5\)	\(-7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+5q^{5}-7q^{7}+37q^{9}-68q^{11}+\cdots\)
2240.4.a.bj	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.e	$1$	$0$	\(0\)	\(8\)	\(5\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+5q^{5}-7q^{7}+37q^{9}+28q^{11}+\cdots\)
2240.4.a.bk	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				35.4.a.a	$1$	$0$	\(0\)	\(8\)	\(5\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+8q^{3}+5q^{5}+7q^{7}+37q^{9}-12q^{11}+\cdots\)
2240.4.a.bl	$2240$	$4$	2240.a	1.a	$1$	$1$	$1$	$132.164$	\(\Q\)	None	✓				140.4.a.f	$1$	$0$	\(0\)	\(9\)	\(-5\)	\(7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{3}-5q^{5}+7q^{7}+54q^{9}+55q^{11}+\cdots\)
2240.4.a.bm	$2240$	$4$	2240.a	1.a	$1$	$2$	$2$	$132.164$	\(\Q(\sqrt{73}) \)	None	✓				280.4.a.e	$1$	$1$	\(0\)	\(-3\)	\(10\)	\(14\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+5q^{5}+7q^{7}+(-8+\cdots)q^{9}+\cdots\)
2240.4.a.bn	$2240$	$4$	2240.a	1.a	$1$	$2$	$2$	$132.164$	\(\Q(\sqrt{2}) \)	None	✓				35.4.a.b	$1$	$1$	\(0\)	\(-2\)	\(10\)	\(-14\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+5q^{5}-7q^{7}+(6-2\beta )q^{9}+\cdots\)
2240.4.a.bo	$2240$	$4$	2240.a	1.a	$1$	$2$	$2$	$132.164$	\(\Q(\sqrt{2}) \)	None	✓				35.4.a.b	$1$	$1$	\(0\)	\(2\)	\(10\)	\(14\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+5q^{5}+7q^{7}+(6+2\beta )q^{9}+\cdots\)
2240.4.a.bp	$2240$	$4$	2240.a	1.a	$1$	$2$	$2$	$132.164$	\(\Q(\sqrt{73}) \)	None	✓				280.4.a.e	$1$	$1$	\(0\)	\(3\)	\(10\)	\(-14\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+5q^{5}-7q^{7}+(-8+3\beta )q^{9}+\cdots\)
2240.4.a.bq	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.11853.1	None	✓				280.4.a.g	$1$	$0$	\(0\)	\(-6\)	\(-15\)	\(21\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}-5q^{5}+7q^{7}+(3-6\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.br	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.11045.1	None	✓				280.4.a.f	$1$	$0$	\(0\)	\(-6\)	\(15\)	\(-21\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+5q^{5}-7q^{7}+(8-7\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bs	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.78693.1	None	✓				280.4.a.i	$1$	$0$	\(0\)	\(-2\)	\(-15\)	\(-21\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-5q^{5}-7q^{7}+(20+\cdots)q^{9}+\cdots\)
2240.4.a.bt	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.14360.1	None	✓				35.4.a.c	$1$	$1$	\(0\)	\(-2\)	\(-15\)	\(21\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2})q^{3}-5q^{5}+7q^{7}+(28+\cdots)q^{9}+\cdots\)
2240.4.a.bu	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.6053.1	None	✓				280.4.a.h	$1$	$0$	\(0\)	\(-2\)	\(15\)	\(21\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+5q^{5}+7q^{7}+(13+\cdots)q^{9}+\cdots\)
2240.4.a.bv	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.14360.1	None	✓				35.4.a.c	$1$	$1$	\(0\)	\(2\)	\(-15\)	\(-21\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{3}-5q^{5}-7q^{7}+(28-3\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bw	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.78693.1	None	✓				280.4.a.i	$1$	$0$	\(0\)	\(2\)	\(-15\)	\(21\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}+7q^{7}+(20-2\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bx	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.6053.1	None	✓				280.4.a.h	$1$	$0$	\(0\)	\(2\)	\(15\)	\(-21\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+5q^{5}-7q^{7}+(13-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.by	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.11853.1	None	✓				280.4.a.g	$1$	$0$	\(0\)	\(6\)	\(-15\)	\(-21\)		$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}-5q^{5}-7q^{7}+(3-6\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.bz	$2240$	$4$	2240.a	1.a	$1$	$3$	$3$	$132.164$	3.3.11045.1	None	✓				280.4.a.f	$1$	$0$	\(0\)	\(6\)	\(15\)	\(21\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+5q^{5}+7q^{7}+(8-7\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.ca	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				1120.4.a.e	$1$	$1$	\(0\)	\(-9\)	\(-20\)	\(-28\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{3}-5q^{5}-7q^{7}+(13+\cdots)q^{9}+\cdots\)
2240.4.a.cb	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	4.4.505876.1	None	✓				1120.4.a.g	$1$	$0$	\(0\)	\(-7\)	\(-20\)	\(28\)		$-$	$+$	$-$	$+$	$2^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{3}-5q^{5}+7q^{7}+(12+\cdots)q^{9}+\cdots\)
2240.4.a.cc	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	4.4.164244.1	None	✓				1120.4.a.f	$1$	$1$	\(0\)	\(-7\)	\(20\)	\(28\)		$-$	$-$	$-$	$-$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{3}+5q^{5}+7q^{7}+(11+\cdots)q^{9}+\cdots\)
2240.4.a.cd	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	4.4.817716.1	None	✓				1120.4.a.h	$1$	$0$	\(0\)	\(-5\)	\(-20\)	\(-28\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-5q^{5}-7q^{7}+(5-2\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.ce	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				1120.4.a.i	$1$	$1$	\(0\)	\(-3\)	\(20\)	\(28\)		$-$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+5q^{5}+7q^{7}+(14+\cdots)q^{9}+\cdots\)
2240.4.a.cf	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				1120.4.a.j	$1$	$1$	\(0\)	\(-1\)	\(20\)	\(-28\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+5q^{5}-7q^{7}+(5+2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.cg	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				1120.4.a.j	$1$	$0$	\(0\)	\(1\)	\(20\)	\(28\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+5q^{5}+7q^{7}+(5+2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.ch	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				1120.4.a.i	$1$	$0$	\(0\)	\(3\)	\(20\)	\(-28\)		$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+5q^{5}-7q^{7}+(14-\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.ci	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	4.4.817716.1	None	✓				1120.4.a.h	$1$	$1$	\(0\)	\(5\)	\(-20\)	\(28\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-5q^{5}+7q^{7}+(5-2\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.cj	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	4.4.505876.1	None	✓				1120.4.a.g	$1$	$1$	\(0\)	\(7\)	\(-20\)	\(-28\)		$-$	$+$	$+$	$-$	$2^{3}\cdot 7$	$\mathrm{SU}(2)$	\(q+(2+\beta _{2})q^{3}-5q^{5}-7q^{7}+(12+\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.ck	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	4.4.164244.1	None	✓				1120.4.a.f	$1$	$0$	\(0\)	\(7\)	\(20\)	\(-28\)		$-$	$-$	$+$	$+$	$2^{3}\cdot 3$	$\mathrm{SU}(2)$	\(q+(2-\beta _{1})q^{3}+5q^{5}-7q^{7}+(11+4\beta _{2}+\cdots)q^{9}+\cdots\)
2240.4.a.cl	$2240$	$4$	2240.a	1.a	$1$	$4$	$4$	$132.164$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				1120.4.a.e	$1$	$0$	\(0\)	\(9\)	\(-20\)	\(28\)		$-$	$+$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(2+\beta _{2})q^{3}-5q^{5}+7q^{7}+(13-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.cm	$2240$	$4$	2240.a	1.a	$1$	$5$	$5$	$132.164$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1120.4.a.q	$1$	$1$	\(0\)	\(-11\)	\(-25\)	\(35\)		$+$	$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{1})q^{3}-5q^{5}+7q^{7}+(13+\cdots)q^{9}+\cdots\)
2240.4.a.cn	$2240$	$4$	2240.a	1.a	$1$	$5$	$5$	$132.164$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1120.4.a.r	$1$	$1$	\(0\)	\(-5\)	\(25\)	\(-35\)		$+$	$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+5q^{5}-7q^{7}+(14+\cdots)q^{9}+\cdots\)
2240.4.a.co	$2240$	$4$	2240.a	1.a	$1$	$5$	$5$	$132.164$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1120.4.a.r	$1$	$0$	\(0\)	\(5\)	\(25\)	\(35\)		$+$	$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+5q^{5}+7q^{7}+(14-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.4.a.cp	$2240$	$4$	2240.a	1.a	$1$	$5$	$5$	$132.164$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1120.4.a.q	$1$	$0$	\(0\)	\(11\)	\(-25\)	\(-35\)		$+$	$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(2+\beta _{1})q^{3}-5q^{5}-7q^{7}+(13+3\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2240))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2240)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 2}\)