Space of modular forms of level 2448, weight 4, and trivial character

• Label: 2448.4.a
• Level: $2448$
• Weight: $4$
• Character orbit: 2448.a
• Rep. character: $\chi_{2448}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $49$
• Sturm bound: $1728$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2448 = 2^{4} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2448.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 49 \)
Sturm bound:			\(1728\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(2448))\).

	Total	New	Old
Modular forms	1320	120	1200
Cusp forms	1272	120	1152
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.

\(2\)	\(3\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(12\)
\(+\)	\(+\)	\(-\)	\(-\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)	\(17\)
\(+\)	\(-\)	\(-\)	\(+\)	\(19\)
\(-\)	\(+\)	\(+\)	\(-\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(19\)
\(-\)	\(-\)	\(-\)	\(-\)	\(17\)
Plus space			\(+\)	\(62\)
Minus space			\(-\)	\(58\)

Trace form

120 * q - 22 * q^7 + 46 * q^11 - 180 * q^19 - 302 * q^23 + 2832 * q^25 - 144 * q^29 + 66 * q^31 + 228 * q^35 - 8 * q^37 + 296 * q^41 - 668 * q^43 - 1368 * q^47 + 6752 * q^49 + 376 * q^53 + 612 * q^55 + 1020 * q^59 - 744 * q^65 - 1440 * q^67 - 1734 * q^71 + 768 * q^73 + 624 * q^77 + 2614 * q^79 + 1340 * q^83 + 248 * q^89 + 984 * q^91 - 4728 * q^95 + 440 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(2448))\) 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	17
2448.4.a.a	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				612.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-17\)	\(-6\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-17q^{5}-6q^{7}-17q^{11}+43q^{13}+\cdots\)
2448.4.a.b	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				51.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-16\)	\(-34\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{5}-34q^{7}-48q^{11}+58q^{13}+\cdots\)
2448.4.a.c	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				34.4.a.b	$1$	$1$	\(0\)	\(0\)	\(-16\)	\(-24\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2^{4}q^{5}-24q^{7}+62q^{11}-62q^{13}+\cdots\)
2448.4.a.d	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				306.4.a.b	$1$	$1$	\(0\)	\(0\)	\(-9\)	\(10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-9q^{5}+10q^{7}-15q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.e	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				408.4.a.a	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(24\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-6q^{5}+24q^{7}+44q^{11}+6q^{13}+\cdots\)
2448.4.a.f	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				17.4.a.a	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(28\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-6q^{5}+28q^{7}-24q^{11}-58q^{13}+\cdots\)
2448.4.a.g	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				102.4.a.d	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-5q^{5}-12q^{7}+37q^{11}+19q^{13}+\cdots\)
2448.4.a.h	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				102.4.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-20\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-20q^{7}-51q^{11}-61q^{13}+\cdots\)
2448.4.a.i	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				204.4.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(16\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2^{4}q^{7}-57q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.j	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				102.4.a.b	$1$	$1$	\(0\)	\(0\)	\(5\)	\(32\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+5q^{5}+2^{5}q^{7}+3^{3}q^{11}-69q^{13}+\cdots\)
2448.4.a.k	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				408.4.a.b	$1$	$1$	\(0\)	\(0\)	\(7\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+7q^{5}-4q^{7}-21q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.l	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				68.4.a.a	$1$	$1$	\(0\)	\(0\)	\(8\)	\(12\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+8q^{5}+12q^{7}-10q^{11}-38q^{13}+\cdots\)
2448.4.a.m	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				306.4.a.b	$1$	$0$	\(0\)	\(0\)	\(9\)	\(10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+9q^{5}+10q^{7}+15q^{11}-5^{2}q^{13}+\cdots\)
2448.4.a.n	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				51.4.a.c	$1$	$0$	\(0\)	\(0\)	\(10\)	\(8\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+10q^{5}+8q^{7}+12q^{11}-26q^{13}+\cdots\)
2448.4.a.o	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				102.4.a.c	$1$	$1$	\(0\)	\(0\)	\(12\)	\(22\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+12q^{5}+22q^{7}-48q^{11}+2q^{13}+\cdots\)
2448.4.a.p	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				612.4.a.a	$1$	$0$	\(0\)	\(0\)	\(17\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+17q^{5}-6q^{7}+17q^{11}+43q^{13}+\cdots\)
2448.4.a.q	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				34.4.a.a	$1$	$0$	\(0\)	\(0\)	\(18\)	\(10\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+18q^{5}+10q^{7}-6q^{11}+74q^{13}+\cdots\)
2448.4.a.r	$2448$	$4$	2448.a	1.a	$1$	$1$	$1$	$144.437$	\(\Q\)	None	✓				51.4.a.b	$1$	$1$	\(0\)	\(0\)	\(20\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+20q^{5}+2q^{7}-48q^{11}-14q^{13}+\cdots\)
2448.4.a.s	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{217}) \)	None	✓				204.4.a.c	$1$	$1$	\(0\)	\(0\)	\(-19\)	\(-18\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-9-\beta )q^{5}+(-8-2\beta )q^{7}+(9-3\beta )q^{11}+\cdots\)
2448.4.a.t	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{15}) \)	None	✓				102.4.a.e	$1$	$0$	\(0\)	\(0\)	\(-12\)	\(-16\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-6+\beta )q^{5}+(-8-\beta )q^{7}+(-12+\cdots)q^{11}+\cdots\)
2448.4.a.u	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{241}) \)	None	✓				408.4.a.c	$1$	$0$	\(0\)	\(0\)	\(-7\)	\(-18\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-3-\beta )q^{5}+(-8-2\beta )q^{7}+(9+3\beta )q^{11}+\cdots\)
2448.4.a.v	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{2}) \)	None	✓				51.4.a.d	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(8\)		$-$	$-$	$-$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+(-3+\beta )q^{5}+(4-\beta )q^{7}+(33+\beta )q^{11}+\cdots\)
2448.4.a.w	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{393}) \)	None	✓				102.4.a.f	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-22\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+(-12+2\beta )q^{7}+(1+\cdots)q^{11}+\cdots\)
2448.4.a.x	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{201}) \)	None	✓				204.4.a.b	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{5}+2\beta q^{7}+(-5-5\beta )q^{11}+\cdots\)
2448.4.a.y	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{13}) \)	None	✓				34.4.a.c	$1$	$0$	\(0\)	\(0\)	\(4\)	\(6\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(2+4\beta )q^{5}+(3+\beta )q^{7}+(-3+15\beta )q^{11}+\cdots\)
2448.4.a.z	$2448$	$4$	2448.a	1.a	$1$	$2$	$2$	$144.437$	\(\Q(\sqrt{3}) \)	None	✓				136.4.a.a	$1$	$1$	\(0\)	\(0\)	\(12\)	\(36\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(6+2\beta )q^{5}+(18+3\beta )q^{7}+(-10+\cdots)q^{11}+\cdots\)
2448.4.a.ba	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.1524.1	None	✓				68.4.a.b	$1$	$0$	\(0\)	\(0\)	\(-26\)	\(-8\)		$-$	$-$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-9+\beta _{1})q^{5}+(-2-3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.bb	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.2747992.1	None	✓				306.4.a.l	$1$	$1$	\(0\)	\(0\)	\(-25\)	\(-18\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-8-\beta _{1})q^{5}+(-6-\beta _{2})q^{7}+(2^{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bc	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.104664.1	None	✓				612.4.a.h	$1$	$0$	\(0\)	\(0\)	\(-19\)	\(10\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-6-\beta _{1})q^{5}+(2+4\beta _{1}-\beta _{2})q^{7}+\cdots\)
2448.4.a.bd	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.5912.1	None	✓				51.4.a.e	$1$	$0$	\(0\)	\(0\)	\(-8\)	\(8\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{1})q^{5}+(2+3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.be	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.23321.1	None	✓				408.4.a.g	$1$	$1$	\(0\)	\(0\)	\(-5\)	\(-20\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-2-\beta _{2})q^{5}+(-7+\beta _{1})q^{7}+(9+\cdots)q^{11}+\cdots\)
2448.4.a.bf	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.1556.1	None	✓				136.4.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-12\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(-4+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2448.4.a.bg	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.12821.1	None	✓				408.4.a.e	$1$	$1$	\(0\)	\(0\)	\(4\)	\(-28\)		$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1}-2\beta _{2})q^{5}+(-9-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.bh	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.4481.1	None	✓				408.4.a.d	$1$	$0$	\(0\)	\(0\)	\(5\)	\(4\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{5}+(2+2\beta _{1})q^{7}+(2^{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bi	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.2636.1	None	✓		✓		17.4.a.b	$1$	$1$	\(0\)	\(0\)	\(8\)	\(-22\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(3-\beta _{2})q^{5}+(-8+\beta _{1}+2\beta _{2})q^{7}+\cdots\)
2448.4.a.bj	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.8396.1	None	✓				136.4.a.b	$1$	$0$	\(0\)	\(0\)	\(8\)	\(2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(3-\beta _{1}+2\beta _{2})q^{5}+(2+3\beta _{1}+\beta _{2})q^{7}+\cdots\)
2448.4.a.bk	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.17717.1	None	✓				408.4.a.f	$1$	$0$	\(0\)	\(0\)	\(10\)	\(22\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(3+\beta _{1})q^{5}+(8-\beta _{1}+\beta _{2})q^{7}+(-11+\cdots)q^{11}+\cdots\)
2448.4.a.bl	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.21324.1	None	✓				204.4.a.d	$1$	$0$	\(0\)	\(0\)	\(19\)	\(8\)		$-$	$-$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(7+\beta _{1}-\beta _{2})q^{5}+(3-\beta _{1}-2\beta _{2})q^{7}+\cdots\)
2448.4.a.bm	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.104664.1	None	✓				612.4.a.h	$1$	$1$	\(0\)	\(0\)	\(19\)	\(10\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(6+\beta _{1})q^{5}+(2+4\beta _{1}-\beta _{2})q^{7}+(14+\cdots)q^{11}+\cdots\)
2448.4.a.bn	$2448$	$4$	2448.a	1.a	$1$	$3$	$3$	$144.437$	3.3.2747992.1	None	✓				306.4.a.l	$1$	$0$	\(0\)	\(0\)	\(25\)	\(-18\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(8+\beta _{1})q^{5}+(-6-\beta _{2})q^{7}+(-2^{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bo	$2448$	$4$	2448.a	1.a	$1$	$4$	$4$	$144.437$	4.4.1506848.1	None	✓		✓		153.4.a.h	$1$	$0$	\(0\)	\(0\)	\(-22\)	\(24\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-5+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(6+3\beta _{1}+\cdots)q^{7}+\cdots\)
2448.4.a.bp	$2448$	$4$	2448.a	1.a	$1$	$4$	$4$	$144.437$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓		✓		408.4.a.h	$1$	$1$	\(0\)	\(0\)	\(-10\)	\(4\)		$+$	$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{5}+(1+\beta _{2}+\beta _{3})q^{7}+\cdots\)
2448.4.a.bq	$2448$	$4$	2448.a	1.a	$1$	$4$	$4$	$144.437$	4.4.550476.1	None	✓				136.4.a.d	$1$	$0$	\(0\)	\(0\)	\(-8\)	\(22\)		$+$	$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(4+2\beta _{1}+\cdots)q^{7}+\cdots\)
2448.4.a.br	$2448$	$4$	2448.a	1.a	$1$	$4$	$4$	$144.437$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓				408.4.a.i	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-32\)		$+$	$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(-9-\beta _{1}+\beta _{2})q^{7}+(15+\cdots)q^{11}+\cdots\)
2448.4.a.bs	$2448$	$4$	2448.a	1.a	$1$	$4$	$4$	$144.437$	4.4.1506848.1	None	✓		✓		153.4.a.h	$1$	$1$	\(0\)	\(0\)	\(22\)	\(24\)		$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(5-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+(6+3\beta _{1}+\cdots)q^{7}+\cdots\)
2448.4.a.bt	$2448$	$4$	2448.a	1.a	$1$	$5$	$5$	$144.437$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1224.4.a.n	$1$	$1$	\(0\)	\(0\)	\(-13\)	\(2\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(-3+\beta _{3})q^{5}-\beta _{1}q^{7}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)
2448.4.a.bu	$2448$	$4$	2448.a	1.a	$1$	$5$	$5$	$144.437$	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)	None	✓				1224.4.a.n	$1$	$0$	\(0\)	\(0\)	\(13\)	\(2\)		$+$	$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+(3-\beta _{3})q^{5}-\beta _{1}q^{7}+(1+\beta _{2}-2\beta _{3}+\cdots)q^{11}+\cdots\)
2448.4.a.bv	$2448$	$4$	2448.a	1.a	$1$	$7$	$7$	$144.437$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		1224.4.a.p	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(-26\)		$+$	$+$	$+$	$+$	$2^{6}\cdot 13$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{5}+(-4-\beta _{3})q^{7}+(9+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
2448.4.a.bw	$2448$	$4$	2448.a	1.a	$1$	$7$	$7$	$144.437$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓		✓		1224.4.a.p	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-26\)		$+$	$+$	$-$	$-$	$2^{6}\cdot 13$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{5}+(-4-\beta _{3})q^{7}+(-9-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(2448))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(2448)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 15}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(1224))\)\(^{\oplus 2}\)