Space of modular forms of level 2496, weight 4, and trivial character

• Label: 2496.4.a
• Level: $2496$
• Weight: $4$
• Character orbit: 2496.a
• Rep. character: $\chi_{2496}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $58$
• Sturm bound: $1792$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2496.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 58 \)
Sturm bound:			\(1792\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2496))\).

	Total	New	Old
Modular forms	1368	144	1224
Cusp forms	1320	144	1176
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.

\(2\)	\(3\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(18\)
\(+\)	\(+\)	\(-\)	\(-\)	\(18\)
\(+\)	\(-\)	\(+\)	\(-\)	\(16\)
\(+\)	\(-\)	\(-\)	\(+\)	\(20\)
\(-\)	\(+\)	\(+\)	\(-\)	\(18\)
\(-\)	\(+\)	\(-\)	\(+\)	\(18\)
\(-\)	\(-\)	\(+\)	\(+\)	\(20\)
\(-\)	\(-\)	\(-\)	\(-\)	\(16\)
Plus space			\(+\)	\(76\)
Minus space			\(-\)	\(68\)

Trace form

\( 144 q + 1296 q^{9} + 3600 q^{25} - 800 q^{29} - 32 q^{37} + 7056 q^{49} + 1504 q^{53} - 1824 q^{61} - 1056 q^{69} + 10816 q^{77} + 11664 q^{81} + 5184 q^{85} - 2976 q^{97}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2496))\) 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	3	13
2496.4.a.a	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.c	$1$	$0$	\(0\)	\(-3\)	\(-10\)	\(-8\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-10q^{5}-8q^{7}+9q^{9}-40q^{11}+\cdots\)
2496.4.a.b	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.e	$1$	$1$	\(0\)	\(-3\)	\(-6\)	\(-20\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-6q^{5}-20q^{7}+9q^{9}+24q^{11}+\cdots\)
2496.4.a.c	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.f	$1$	$1$	\(0\)	\(-3\)	\(-4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-4q^{5}+4q^{7}+9q^{9}-2q^{11}+\cdots\)
2496.4.a.d	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				156.4.a.b	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(-32\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}-2^{5}q^{7}+9q^{9}+68q^{11}+\cdots\)
2496.4.a.e	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				156.4.a.a	$1$	$1$	\(0\)	\(-3\)	\(6\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+6q^{5}+4q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
2496.4.a.f	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				39.4.a.a	$1$	$1$	\(0\)	\(-3\)	\(12\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+12q^{5}-2q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
2496.4.a.g	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.a	$1$	$0$	\(0\)	\(-3\)	\(16\)	\(-28\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2^{4}q^{5}-28q^{7}+9q^{9}+34q^{11}+\cdots\)
2496.4.a.h	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.b	$1$	$1$	\(0\)	\(-3\)	\(16\)	\(-8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2^{4}q^{5}-8q^{7}+9q^{9}+38q^{11}+\cdots\)
2496.4.a.i	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.d	$1$	$0$	\(0\)	\(-3\)	\(20\)	\(32\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+20q^{5}+2^{5}q^{7}+9q^{9}+50q^{11}+\cdots\)
2496.4.a.j	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.c	$1$	$0$	\(0\)	\(3\)	\(-10\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-10q^{5}+8q^{7}+9q^{9}+40q^{11}+\cdots\)
2496.4.a.k	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.e	$1$	$1$	\(0\)	\(3\)	\(-6\)	\(20\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-6q^{5}+20q^{7}+9q^{9}-24q^{11}+\cdots\)
2496.4.a.l	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.f	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-4q^{5}-4q^{7}+9q^{9}+2q^{11}+\cdots\)
2496.4.a.m	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				156.4.a.b	$1$	$0$	\(0\)	\(3\)	\(2\)	\(32\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{5}+2^{5}q^{7}+9q^{9}-68q^{11}+\cdots\)
2496.4.a.n	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				156.4.a.a	$1$	$1$	\(0\)	\(3\)	\(6\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+6q^{5}-4q^{7}+9q^{9}-6^{2}q^{11}+\cdots\)
2496.4.a.o	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				39.4.a.a	$1$	$1$	\(0\)	\(3\)	\(12\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+12q^{5}+2q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
2496.4.a.p	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.b	$1$	$1$	\(0\)	\(3\)	\(16\)	\(8\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2^{4}q^{5}+8q^{7}+9q^{9}-38q^{11}+\cdots\)
2496.4.a.q	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.a	$1$	$0$	\(0\)	\(3\)	\(16\)	\(28\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2^{4}q^{5}+28q^{7}+9q^{9}-34q^{11}+\cdots\)
2496.4.a.r	$2496$	$4$	2496.a	1.a	$1$	$1$	$1$	$147.269$	\(\Q\)	None	✓				78.4.a.d	$1$	$0$	\(0\)	\(3\)	\(20\)	\(-32\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+20q^{5}-2^{5}q^{7}+9q^{9}-50q^{11}+\cdots\)
2496.4.a.s	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{14}) \)	None	✓				39.4.a.b	$1$	$0$	\(0\)	\(-6\)	\(-24\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-12+\beta )q^{5}+\beta q^{7}+9q^{9}+\cdots\)
2496.4.a.t	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{10}) \)	None	✓				156.4.a.d	$1$	$1$	\(0\)	\(-6\)	\(-24\)	\(8\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-12+\beta )q^{5}+(4+3\beta )q^{7}+\cdots\)
2496.4.a.u	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{43}) \)	None	✓				312.4.a.f	$1$	$1$	\(0\)	\(-6\)	\(-12\)	\(44\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-6+\beta )q^{5}+(22-\beta )q^{7}+\cdots\)
2496.4.a.v	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{113}) \)	None	✓				312.4.a.c	$1$	$1$	\(0\)	\(-6\)	\(-6\)	\(10\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-3-\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.w	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{22}) \)	None	✓				156.4.a.c	$1$	$0$	\(0\)	\(-6\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+\beta q^{5}+(-4-3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.x	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{55}) \)	None	✓				312.4.a.b	$1$	$0$	\(0\)	\(-6\)	\(4\)	\(-20\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2+\beta )q^{5}+(-10+\beta )q^{7}+\cdots\)
2496.4.a.y	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{7}) \)	None	✓				312.4.a.e	$1$	$1$	\(0\)	\(-6\)	\(4\)	\(-20\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2+\beta )q^{5}+(-10+3\beta )q^{7}+\cdots\)
2496.4.a.z	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{3}) \)	None	✓				312.4.a.a	$1$	$0$	\(0\)	\(-6\)	\(4\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2+\beta )q^{5}+(-2-3\beta )q^{7}+\cdots\)
2496.4.a.ba	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{17}) \)	None	✓				312.4.a.d	$1$	$0$	\(0\)	\(-6\)	\(18\)	\(-10\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-3q^{3}+(9-\beta )q^{5}+(-5-5\beta )q^{7}+\cdots\)
2496.4.a.bb	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{10}) \)	None	✓				156.4.a.d	$1$	$1$	\(0\)	\(6\)	\(-24\)	\(-8\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-12+\beta )q^{5}+(-4-3\beta )q^{7}+\cdots\)
2496.4.a.bc	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{14}) \)	None	✓				39.4.a.b	$1$	$0$	\(0\)	\(6\)	\(-24\)	\(0\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-12+\beta )q^{5}-\beta q^{7}+9q^{9}+\cdots\)
2496.4.a.bd	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{43}) \)	None	✓				312.4.a.f	$1$	$1$	\(0\)	\(6\)	\(-12\)	\(-44\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-6+\beta )q^{5}+(-22+\beta )q^{7}+\cdots\)
2496.4.a.be	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{113}) \)	None	✓				312.4.a.c	$1$	$1$	\(0\)	\(6\)	\(-6\)	\(-10\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-3-\beta )q^{5}+(-5-\beta )q^{7}+\cdots\)
2496.4.a.bf	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{22}) \)	None	✓				156.4.a.c	$1$	$0$	\(0\)	\(6\)	\(0\)	\(8\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+\beta q^{5}+(4+3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bg	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{3}) \)	None	✓				312.4.a.a	$1$	$0$	\(0\)	\(6\)	\(4\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2+\beta )q^{5}+(2+3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bh	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{7}) \)	None	✓				312.4.a.e	$1$	$1$	\(0\)	\(6\)	\(4\)	\(20\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2+\beta )q^{5}+(10-3\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bi	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{55}) \)	None	✓				312.4.a.b	$1$	$0$	\(0\)	\(6\)	\(4\)	\(20\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2+\beta )q^{5}+(10-\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bj	$2496$	$4$	2496.a	1.a	$1$	$2$	$2$	$147.269$	\(\Q(\sqrt{17}) \)	None	✓				312.4.a.d	$1$	$0$	\(0\)	\(6\)	\(18\)	\(10\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+3q^{3}+(9-\beta )q^{5}+(5+5\beta )q^{7}+9q^{9}+\cdots\)
2496.4.a.bk	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.36248.1	None	✓				312.4.a.g	$1$	$1$	\(0\)	\(-9\)	\(-16\)	\(22\)		$-$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-5-\beta _{2})q^{5}+(8-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2496.4.a.bl	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.3144.1	None	✓				39.4.a.c	$1$	$0$	\(0\)	\(-9\)	\(-4\)	\(30\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-1+\beta _{2})q^{5}+(11+3\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bm	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.13916.1	None	✓				312.4.a.h	$1$	$0$	\(0\)	\(-9\)	\(4\)	\(6\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{1}+\beta _{2})q^{7}+\cdots\)
2496.4.a.bn	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.3261.1	None	✓				1248.4.a.a	$1$	$0$	\(0\)	\(-9\)	\(10\)	\(0\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(3-\beta _{1})q^{5}+(-1-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
2496.4.a.bo	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.36248.1	None	✓				312.4.a.g	$1$	$1$	\(0\)	\(9\)	\(-16\)	\(-22\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-5-\beta _{2})q^{5}+(-8+\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bp	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.3144.1	None	✓				39.4.a.c	$1$	$0$	\(0\)	\(9\)	\(-4\)	\(-30\)		$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-1+\beta _{2})q^{5}+(-11-3\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bq	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.13916.1	None	✓				312.4.a.h	$1$	$0$	\(0\)	\(9\)	\(4\)	\(-6\)		$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(1-\beta _{2})q^{5}+(-2-\beta _{1}-\beta _{2})q^{7}+\cdots\)
2496.4.a.br	$2496$	$4$	2496.a	1.a	$1$	$3$	$3$	$147.269$	3.3.3261.1	None	✓				1248.4.a.a	$1$	$1$	\(0\)	\(9\)	\(10\)	\(0\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(3-\beta _{1})q^{5}+(1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
2496.4.a.bs	$2496$	$4$	2496.a	1.a	$1$	$4$	$4$	$147.269$	4.4.6406729.1	None	✓				1248.4.a.d	$1$	$0$	\(0\)	\(-12\)	\(-2\)	\(18\)		$-$	$+$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-3q^{3}+\beta _{2}q^{5}+(5-\beta _{3})q^{7}+9q^{9}+\cdots\)
2496.4.a.bt	$2496$	$4$	2496.a	1.a	$1$	$4$	$4$	$147.269$	4.4.236113.1	None	✓				1248.4.a.c	$1$	$0$	\(0\)	\(-12\)	\(2\)	\(10\)		$-$	$+$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(1+\beta _{2})q^{5}+(3+\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
2496.4.a.bu	$2496$	$4$	2496.a	1.a	$1$	$4$	$4$	$147.269$	4.4.6406729.1	None	✓				1248.4.a.d	$1$	$1$	\(0\)	\(12\)	\(-2\)	\(-18\)		$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+3q^{3}+\beta _{2}q^{5}+(-5+\beta _{3})q^{7}+9q^{9}+\cdots\)
2496.4.a.bv	$2496$	$4$	2496.a	1.a	$1$	$4$	$4$	$147.269$	4.4.236113.1	None	✓				1248.4.a.c	$1$	$1$	\(0\)	\(12\)	\(2\)	\(-10\)		$-$	$-$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(1+\beta _{2})q^{5}+(-3-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
2496.4.a.bw	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.k	$1$	$1$	\(0\)	\(-15\)	\(-10\)	\(-14\)		$+$	$+$	$-$	$-$	$2^{8}\cdot 5$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-2-\beta _{2})q^{5}+(-3+\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.bx	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1248.4.a.j	$1$	$0$	\(0\)	\(-15\)	\(-10\)	\(0\)		$+$	$+$	$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-2+\beta _{1})q^{5}-\beta _{3}q^{7}+9q^{9}+\cdots\)
2496.4.a.by	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.i	$1$	$1$	\(0\)	\(-15\)	\(-8\)	\(38\)		$-$	$+$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(-2+\beta _{1})q^{5}+(8-\beta _{4})q^{7}+\cdots\)
2496.4.a.bz	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.h	$1$	$1$	\(0\)	\(-15\)	\(8\)	\(-38\)		$-$	$+$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2+\beta _{2}-\beta _{3})q^{5}+(-7+\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.ca	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.g	$1$	$1$	\(0\)	\(-15\)	\(10\)	\(-14\)		$+$	$+$	$-$	$-$	$2^{8}$	$\mathrm{SU}(2)$	\(q-3q^{3}+(2-\beta _{2})q^{5}+(-3-\beta _{3}-\beta _{4})q^{7}+\cdots\)
2496.4.a.cb	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓		✓		1248.4.a.j	$1$	$1$	\(0\)	\(15\)	\(-10\)	\(0\)		$+$	$-$	$+$	$-$	$2^{7}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-2+\beta _{1})q^{5}+\beta _{3}q^{7}+9q^{9}+\cdots\)
2496.4.a.cc	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.k	$1$	$0$	\(0\)	\(15\)	\(-10\)	\(14\)		$+$	$-$	$-$	$+$	$2^{8}\cdot 5$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-2-\beta _{2})q^{5}+(3-\beta _{1})q^{7}+\cdots\)
2496.4.a.cd	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.i	$1$	$0$	\(0\)	\(15\)	\(-8\)	\(-38\)		$-$	$-$	$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(-2+\beta _{1})q^{5}+(-8+\beta _{4})q^{7}+\cdots\)
2496.4.a.ce	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.h	$1$	$0$	\(0\)	\(15\)	\(8\)	\(38\)		$-$	$-$	$+$	$+$	$2^{7}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2+\beta _{2}-\beta _{3})q^{5}+(7-\beta _{1}+\cdots)q^{7}+\cdots\)
2496.4.a.cf	$2496$	$4$	2496.a	1.a	$1$	$5$	$5$	$147.269$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1248.4.a.g	$1$	$0$	\(0\)	\(15\)	\(10\)	\(14\)		$+$	$-$	$-$	$+$	$2^{8}$	$\mathrm{SU}(2)$	\(q+3q^{3}+(2-\beta _{2})q^{5}+(3+\beta _{3}+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2496))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2496)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(832))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)