Space of modular forms of level 4864, weight 2, and trivial character

• Label: 4864.2.a
• Level: $4864$
• Weight: $2$
• Character orbit: 4864.a
• Rep. character: $\chi_{4864}(1,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Newform subspaces: $46$
• Sturm bound: $1280$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4864 = 2^{8} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4864.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 46 \)
Sturm bound:			\(1280\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4864))\).

	Total	New	Old
Modular forms	664	144	520
Cusp forms	617	144	473
Eisenstein series	47	0	47

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

\(2\)	\(19\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(34\)
\(+\)	\(-\)	$-$	\(40\)
\(-\)	\(+\)	$-$	\(38\)
\(-\)	\(-\)	$+$	\(32\)
Plus space		\(+\)	\(66\)
Minus space		\(-\)	\(78\)

Trace form

\( 144 q + 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4864))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	19
4864.2.a.a	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-3\)	\(-4\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-4q^{5}+q^{7}+6q^{9}-5q^{13}+\cdots\)
4864.2.a.b	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-3\)	\(4\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+4q^{5}-q^{7}+6q^{9}+5q^{13}+\cdots\)
4864.2.a.c	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}-q^{7}-2q^{9}-4q^{11}+\cdots\)
4864.2.a.d	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-3q^{7}-2q^{9}-3q^{13}+3q^{17}+\cdots\)
4864.2.a.e	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+3q^{7}-2q^{9}+3q^{13}+3q^{17}+\cdots\)
4864.2.a.f	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
4864.2.a.g	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
4864.2.a.h	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{7}-3q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
4864.2.a.i	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
4864.2.a.j	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{7}-3q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
4864.2.a.k	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{7}-2q^{9}+4q^{11}+\cdots\)
4864.2.a.l	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{7}-2q^{9}+3q^{13}+3q^{17}+\cdots\)
4864.2.a.m	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{7}-2q^{9}-3q^{13}+3q^{17}+\cdots\)
4864.2.a.n	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots\)
4864.2.a.o	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(-4\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-4q^{5}-q^{7}+6q^{9}-5q^{13}+\cdots\)
4864.2.a.p	$4864$	$2$	4864.a	1.a	$1$	$1$	$1$	$38.839$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(4\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+4q^{5}+q^{7}+6q^{9}+5q^{13}+\cdots\)
4864.2.a.q	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+3q^{11}+\cdots\)
4864.2.a.r	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{11}) \)	None	✓	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+5q^{11}+\cdots\)
4864.2.a.s	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(2\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+(1+\beta )q^{7}-2q^{9}+4q^{11}+\cdots\)
4864.2.a.t	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2\beta q^{5}-\beta q^{7}-2q^{9}+3\beta q^{13}+\cdots\)
4864.2.a.u	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(-2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+(-1+\beta )q^{7}-2q^{9}+\cdots\)
4864.2.a.v	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+(-1+\beta )q^{7}-2q^{9}+\cdots\)
4864.2.a.w	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2\beta q^{5}+\beta q^{7}-2q^{9}+3\beta q^{13}+\cdots\)
4864.2.a.x	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(4\)	\(2\)		$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+(1-\beta )q^{7}-2q^{9}-4q^{11}+\cdots\)
4864.2.a.y	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{11}) \)	None	✓	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-5q^{11}+\cdots\)
4864.2.a.z	$4864$	$2$	4864.a	1.a	$1$	$2$	$2$	$38.839$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$1$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-3q^{11}+\cdots\)
4864.2.a.ba	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+\cdots\)
4864.2.a.bb	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1})q^{5}+\cdots\)
4864.2.a.bc	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
4864.2.a.bd	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(2\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4864.2.a.be	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4864.2.a.bf	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.892.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
4864.2.a.bg	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+\cdots\)
4864.2.a.bh	$4864$	$2$	4864.a	1.a	$1$	$3$	$3$	$38.839$	3.3.316.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4864.2.a.bi	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4864.2.a.bj	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	\(\Q(\sqrt{3}, \sqrt{19})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+(-2-\beta _{3})q^{11}+\cdots\)
4864.2.a.bk	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	\(\Q(\sqrt{3}, \sqrt{19})\)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}-3q^{9}+(2+\beta _{3})q^{11}+\cdots\)
4864.2.a.bl	$4864$	$2$	4864.a	1.a	$1$	$4$	$4$	$38.839$	\(\Q(\sqrt{3}, \sqrt{11})\)	None	✓	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{3})q^{3}-\beta _{1}q^{5}+(2\beta _{1}-\beta _{2})q^{7}+\cdots\)
4864.2.a.bm	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	8.8.\(\cdots\).1	None	✓	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$-$	$-$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{7})q^{9}+\cdots\)
4864.2.a.bn	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(-4\)		$-$	$-$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}-\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
4864.2.a.bo	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-8\)	\(4\)		$+$	$+$	$+$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
4864.2.a.bp	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(8\)	\(-4\)		$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{5}q^{3}+(1-\beta _{2})q^{5}-\beta _{4}q^{7}+(1-\beta _{7})q^{9}+\cdots\)
4864.2.a.bq	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(8\)	\(4\)		$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{5}q^{3}+(1-\beta _{2})q^{5}+\beta _{4}q^{7}+(1-\beta _{7})q^{9}+\cdots\)
4864.2.a.br	$4864$	$2$	4864.a	1.a	$1$	$8$	$8$	$38.839$	8.8.\(\cdots\).1	None	✓	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$-$	$+$	$-$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{7})q^{9}+\cdots\)
4864.2.a.bs	$4864$	$2$	4864.a	1.a	$1$	$10$	$10$	$38.839$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$1$	\(0\)	\(-4\)	\(0\)	\(0\)		$+$	$+$	$+$	$2^{6}$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
4864.2.a.bt	$4864$	$2$	4864.a	1.a	$1$	$10$	$10$	$38.839$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$+$	$-$	$-$	$2^{6}$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2432))\)\(^{\oplus 2}\)