Space of modular forms of level 4896, weight 2, and trivial character

• Label: 4896.2.a
• Level: $4896$
• Weight: $2$
• Character orbit: 4896.a
• Rep. character: $\chi_{4896}(1,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $38$
• Sturm bound: $1728$
• Trace bound: $29$

Defining parameters

Level:	\( N \)	\(=\)	\( 4896 = 2^{5} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4896.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 38 \)
Sturm bound:			\(1728\)
Trace bound:			\(29\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4896))\).

	Total	New	Old
Modular forms	896	80	816
Cusp forms	833	80	753
Eisenstein series	63	0	63

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		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(106\)	\(6\)	\(100\)		\(99\)	\(6\)	\(93\)		\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)		\(114\)	\(10\)	\(104\)		\(106\)	\(10\)	\(96\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(+\)	\(-\)		\(116\)	\(13\)	\(103\)		\(108\)	\(13\)	\(95\)		\(8\)	\(0\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)		\(108\)	\(11\)	\(97\)		\(100\)	\(11\)	\(89\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(+\)	\(-\)		\(118\)	\(10\)	\(108\)		\(110\)	\(10\)	\(100\)		\(8\)	\(0\)	\(8\)
\(-\)	\(+\)	\(-\)	\(+\)		\(110\)	\(6\)	\(104\)		\(102\)	\(6\)	\(96\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(+\)	\(+\)		\(108\)	\(11\)	\(97\)		\(100\)	\(11\)	\(89\)		\(8\)	\(0\)	\(8\)
\(-\)	\(-\)	\(-\)	\(-\)		\(116\)	\(13\)	\(103\)		\(108\)	\(13\)	\(95\)		\(8\)	\(0\)	\(8\)
Plus space			\(+\)		\(432\)	\(34\)	\(398\)		\(401\)	\(34\)	\(367\)		\(31\)	\(0\)	\(31\)
Minus space			\(-\)		\(464\)	\(46\)	\(418\)		\(432\)	\(46\)	\(386\)		\(32\)	\(0\)	\(32\)

Trace form

\( 80 q + 16 q^{13} + 64 q^{25} - 16 q^{29} + 16 q^{37} + 16 q^{41} + 96 q^{49} + 48 q^{53} + 16 q^{61} - 16 q^{65} - 16 q^{77} + 80 q^{89} + 80 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4896))\) 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
4896.2.a.a	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				544.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-2q^{11}+2q^{13}+q^{17}+\cdots\)
4896.2.a.b	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				544.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+4q^{7}+2q^{11}+2q^{13}+q^{17}+\cdots\)
4896.2.a.c	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				544.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{7}-2q^{11}+2q^{13}-q^{17}+\cdots\)
4896.2.a.d	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-4q^{11}-2q^{13}-q^{17}-8q^{23}+\cdots\)
4896.2.a.e	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+4q^{11}-2q^{13}-q^{17}+8q^{23}+\cdots\)
4896.2.a.f	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				544.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+2q^{7}+2q^{11}+2q^{13}-q^{17}+\cdots\)
4896.2.a.g	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}+5q^{11}-q^{13}+q^{17}+\cdots\)
4896.2.a.h	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-5q^{11}-q^{13}+q^{17}+\cdots\)
4896.2.a.i	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.d	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-6q^{13}+q^{17}+4q^{19}+6q^{23}+\cdots\)
4896.2.a.j	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				544.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}+4q^{11}+2q^{13}+q^{17}-4q^{19}+\cdots\)
4896.2.a.k	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				544.2.a.c	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-4q^{11}+2q^{13}+q^{17}+4q^{19}+\cdots\)
4896.2.a.l	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.d	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-6q^{13}+q^{17}-4q^{19}-6q^{23}+\cdots\)
4896.2.a.m	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.b	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-5q^{11}-5q^{13}-q^{17}+\cdots\)
4896.2.a.n	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}+q^{11}-q^{13}-q^{17}+\cdots\)
4896.2.a.o	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-q^{11}-q^{13}-q^{17}+\cdots\)
4896.2.a.p	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+5q^{11}-5q^{13}-q^{17}+\cdots\)
4896.2.a.q	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.a	$1$	$1$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}-2q^{7}-3q^{11}+3q^{13}+q^{17}+\cdots\)
4896.2.a.r	$4896$	$2$	4896.a	1.a	$1$	$1$	$1$	$39.095$	\(\Q\)	None	✓				1632.2.a.a	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{5}+2q^{7}+3q^{11}+3q^{13}+q^{17}+\cdots\)
4896.2.a.s	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{5}) \)	None	✓	✓			4896.2.a.s	$2$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{5}-\beta q^{11}-q^{13}+q^{17}+\beta q^{19}+\cdots\)
4896.2.a.t	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{33}) \)	None	✓				1632.2.a.n	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}-2q^{7}-\beta q^{11}+(2+\beta )q^{13}+\cdots\)
4896.2.a.u	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{33}) \)	None	✓				1632.2.a.n	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+2q^{7}+\beta q^{11}+(2+\beta )q^{13}+\cdots\)
4896.2.a.v	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{5}) \)	None	✓	✓			4896.2.a.s	$2$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{11}-q^{13}-q^{17}+\beta q^{19}+\cdots\)
4896.2.a.w	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{17}) \)	None	✓				1632.2.a.m	$1$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(-2+2\beta )q^{7}+(-1+\beta )q^{11}+\cdots\)
4896.2.a.x	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{17}) \)	None	✓				1632.2.a.m	$1$	$0$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}+(2-2\beta )q^{7}+(1-\beta )q^{11}+\cdots\)
4896.2.a.y	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{10}) \)	None	✓				544.2.a.h	$2$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+\beta q^{7}-\beta q^{11}-4q^{13}+q^{17}+\cdots\)
4896.2.a.z	$4896$	$2$	4896.a	1.a	$1$	$2$	$2$	$39.095$	\(\Q(\sqrt{2}) \)	None	✓				544.2.a.g	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3\beta q^{7}-\beta q^{11}-4q^{13}+q^{17}+\cdots\)
4896.2.a.ba	$4896$	$2$	4896.a	1.a	$1$	$3$	$3$	$39.095$	3.3.316.1	None	✓				1632.2.a.r	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
4896.2.a.bb	$4896$	$2$	4896.a	1.a	$1$	$3$	$3$	$39.095$	3.3.316.1	None	✓				1632.2.a.r	$1$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
4896.2.a.bc	$4896$	$2$	4896.a	1.a	$1$	$3$	$3$	$39.095$	3.3.229.1	None	✓				1632.2.a.q	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-2q^{7}+(-1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
4896.2.a.bd	$4896$	$2$	4896.a	1.a	$1$	$3$	$3$	$39.095$	3.3.229.1	None	✓				1632.2.a.q	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+2q^{7}+(1+\beta _{1}+\beta _{2})q^{11}+\cdots\)
4896.2.a.be	$4896$	$2$	4896.a	1.a	$1$	$3$	$3$	$39.095$	3.3.148.1	None	✓				544.2.a.i	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+(3+\beta _{1}+\cdots)q^{11}+\cdots\)
4896.2.a.bf	$4896$	$2$	4896.a	1.a	$1$	$3$	$3$	$39.095$	3.3.148.1	None	✓				544.2.a.i	$1$	$1$	\(0\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(\beta _{1}+\beta _{2})q^{5}+(1-\beta _{2})q^{7}+(-3-\beta _{1}+\cdots)q^{11}+\cdots\)
4896.2.a.bg	$4896$	$2$	4896.a	1.a	$1$	$4$	$4$	$39.095$	4.4.13768.1	None	✓	✓	✓		4896.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{11}+\cdots\)
4896.2.a.bh	$4896$	$2$	4896.a	1.a	$1$	$4$	$4$	$39.095$	4.4.13768.1	None	✓	✓			4896.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{5}+(1-\beta _{1})q^{7}+(-1+\cdots)q^{11}+\cdots\)
4896.2.a.bi	$4896$	$2$	4896.a	1.a	$1$	$4$	$4$	$39.095$	4.4.13768.1	None	✓	✓	✓		4896.2.a.bg	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-4\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(-1+\beta _{1})q^{7}+(-1+\cdots)q^{11}+\cdots\)
4896.2.a.bj	$4896$	$2$	4896.a	1.a	$1$	$4$	$4$	$39.095$	4.4.13768.1	None	✓	✓			4896.2.a.bg	$1$	$0$	\(0\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{5}+(1-\beta _{1})q^{7}+(1+\beta _{2}+\cdots)q^{11}+\cdots\)
4896.2.a.bk	$4896$	$2$	4896.a	1.a	$1$	$6$	$6$	$39.095$	6.6.102503232.1	None	✓	✓	✓		4896.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$-$	$+$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}-\beta _{5}q^{11}+\cdots\)
4896.2.a.bl	$4896$	$2$	4896.a	1.a	$1$	$6$	$6$	$39.095$	6.6.102503232.1	None	✓	✓	✓		4896.2.a.bk	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$+$	$-$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{5}+\beta _{2}q^{7}-\beta _{5}q^{11}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4896))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4896)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(306))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(544))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(612))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1632))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2448))\)\(^{\oplus 2}\)