Space of modular forms of level 5720, weight 2, and trivial character

• Label: 5720.2.a
• Level: $5720$
• Weight: $2$
• Character orbit: 5720.a
• Rep. character: $\chi_{5720}(1,\cdot)$
• Character field: $\Q$
• Dimension: $120$
• Newform subspaces: $29$
• Sturm bound: $2016$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 5720 = 2^{3} \cdot 5 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5720.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 29 \)
Sturm bound:			\(2016\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5720))\).

	Total	New	Old
Modular forms	1024	120	904
Cusp forms	993	120	873
Eisenstein series	31	0	31

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

\(2\)	\(5\)	\(11\)	\(13\)	Fricke		Total				Cusp				Eisenstein
						All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)		\(58\)	\(8\)	\(50\)		\(57\)	\(8\)	\(49\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)		\(65\)	\(8\)	\(57\)		\(63\)	\(8\)	\(55\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)		\(69\)	\(7\)	\(62\)		\(67\)	\(7\)	\(60\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)		\(62\)	\(6\)	\(56\)		\(60\)	\(6\)	\(54\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)		\(67\)	\(7\)	\(60\)		\(65\)	\(7\)	\(58\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)		\(66\)	\(7\)	\(59\)		\(64\)	\(7\)	\(57\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)		\(62\)	\(8\)	\(54\)		\(60\)	\(8\)	\(52\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)		\(63\)	\(9\)	\(54\)		\(61\)	\(9\)	\(52\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)		\(66\)	\(8\)	\(58\)		\(64\)	\(8\)	\(56\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)		\(59\)	\(5\)	\(54\)		\(57\)	\(5\)	\(52\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)		\(63\)	\(6\)	\(57\)		\(61\)	\(6\)	\(55\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)		\(70\)	\(10\)	\(60\)		\(68\)	\(10\)	\(58\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)		\(65\)	\(7\)	\(58\)		\(63\)	\(7\)	\(56\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)		\(66\)	\(10\)	\(56\)		\(64\)	\(10\)	\(54\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)		\(62\)	\(9\)	\(53\)		\(60\)	\(9\)	\(51\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)		\(61\)	\(5\)	\(56\)		\(59\)	\(5\)	\(54\)		\(2\)	\(0\)	\(2\)
Plus space				\(+\)		\(496\)	\(52\)	\(444\)		\(481\)	\(52\)	\(429\)		\(15\)	\(0\)	\(15\)
Minus space				\(-\)		\(528\)	\(68\)	\(460\)		\(512\)	\(68\)	\(444\)		\(16\)	\(0\)	\(16\)

Trace form

120 * q + 4 * q^5 + 128 * q^9 - 16 * q^21 + 120 * q^25 - 24 * q^29 + 8 * q^33 + 24 * q^37 + 24 * q^41 - 12 * q^45 + 160 * q^49 + 16 * q^53 + 16 * q^59 + 24 * q^61 - 8 * q^67 - 32 * q^71 + 16 * q^73 + 32 * q^79 + 120 * q^81 - 32 * q^83 + 16 * q^87 - 24 * q^89 + 16 * q^93 + 16 * q^95 + 64 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5720))\) 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	11	13
5720.2.a.a	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}-q^{11}+q^{13}+\cdots\)
5720.2.a.b	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+q^{11}-q^{13}-2q^{17}+\cdots\)
5720.2.a.c	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.c	$1$	$0$	\(0\)	\(0\)	\(1\)	\(4\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+4q^{7}-3q^{9}-q^{11}-q^{13}+\cdots\)
5720.2.a.d	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.d	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-5q^{7}-2q^{9}-q^{11}-q^{13}+\cdots\)
5720.2.a.e	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.e	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
5720.2.a.f	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.f	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-2q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
5720.2.a.g	$5720$	$2$	5720.a	1.a	$1$	$1$	$1$	$45.674$	\(\Q\)	None	✓	✓			5720.2.a.g	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
5720.2.a.h	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{3}) \)	None	✓	✓			5720.2.a.h	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
5720.2.a.i	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{13}) \)	None	✓	✓			5720.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(5\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(3-\beta )q^{7}+\beta q^{9}+q^{11}+\cdots\)
5720.2.a.j	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{5}) \)	None	✓	✓			5720.2.a.j	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-1\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(1-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
5720.2.a.k	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{5}) \)	None	✓	✓			5720.2.a.k	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(5\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(3-\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
5720.2.a.l	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{33}) \)	None	✓	✓			5720.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+q^{11}-q^{13}+(3-\beta )q^{17}+\cdots\)
5720.2.a.m	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{33}) \)	None	✓	✓			5720.2.a.m	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(1\)		$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+\beta q^{7}+(5+\beta )q^{9}+q^{11}+\cdots\)
5720.2.a.n	$5720$	$2$	5720.a	1.a	$1$	$2$	$2$	$45.674$	\(\Q(\sqrt{5}) \)	None	✓	✓			5720.2.a.n	$1$	$1$	\(0\)	\(3\)	\(-2\)	\(-1\)		$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}-\beta q^{7}+(-1+3\beta )q^{9}+\cdots\)
5720.2.a.o	$5720$	$2$	5720.a	1.a	$1$	$3$	$3$	$45.674$	3.3.148.1	None	✓	✓			5720.2.a.o	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}-q^{5}+(-2+2\beta _{1}+\cdots)q^{7}+\cdots\)
5720.2.a.p	$5720$	$2$	5720.a	1.a	$1$	$3$	$3$	$45.674$	3.3.316.1	None	✓	✓	✓		5720.2.a.p	$1$	$1$	\(0\)	\(-1\)	\(3\)	\(-5\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-2+\beta _{1})q^{7}+\beta _{2}q^{9}+\cdots\)
5720.2.a.q	$5720$	$2$	5720.a	1.a	$1$	$3$	$3$	$45.674$	3.3.229.1	None	✓	✓			5720.2.a.q	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(0\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{3}-q^{5}-\beta _{1}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
5720.2.a.r	$5720$	$2$	5720.a	1.a	$1$	$4$	$4$	$45.674$	4.4.69272.1	None	✓	✓	✓		5720.2.a.r	$1$	$1$	\(0\)	\(0\)	\(4\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-\beta _{1}q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5720.2.a.s	$5720$	$2$	5720.a	1.a	$1$	$5$	$5$	$45.674$	5.5.3696856.1	None	✓	✓	✓		5720.2.a.s	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+\beta _{4}q^{7}+\beta _{2}q^{9}+q^{11}+\cdots\)
5720.2.a.t	$5720$	$2$	5720.a	1.a	$1$	$6$	$6$	$45.674$	6.6.98351993.1	None	✓	✓	✓		5720.2.a.t	$1$	$0$	\(0\)	\(0\)	\(6\)	\(0\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(1+\beta _{2})q^{9}+\cdots\)
5720.2.a.u	$5720$	$2$	5720.a	1.a	$1$	$7$	$7$	$45.674$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		5720.2.a.u	$1$	$1$	\(0\)	\(-5\)	\(7\)	\(-7\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
5720.2.a.v	$5720$	$2$	5720.a	1.a	$1$	$7$	$7$	$45.674$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.v	$1$	$1$	\(0\)	\(-4\)	\(7\)	\(-6\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{4})q^{7}+\cdots\)
5720.2.a.w	$5720$	$2$	5720.a	1.a	$1$	$7$	$7$	$45.674$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		5720.2.a.w	$1$	$0$	\(0\)	\(-3\)	\(-7\)	\(5\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{5})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
5720.2.a.x	$5720$	$2$	5720.a	1.a	$1$	$8$	$8$	$45.674$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.x	$1$	$1$	\(0\)	\(-1\)	\(-8\)	\(-1\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}-\beta _{7}q^{7}+(1+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
5720.2.a.y	$5720$	$2$	5720.a	1.a	$1$	$8$	$8$	$45.674$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.y	$1$	$0$	\(0\)	\(1\)	\(-8\)	\(5\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{6})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
5720.2.a.z	$5720$	$2$	5720.a	1.a	$1$	$9$	$9$	$45.674$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.z	$1$	$0$	\(0\)	\(4\)	\(9\)	\(6\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{6})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
5720.2.a.ba	$5720$	$2$	5720.a	1.a	$1$	$9$	$9$	$45.674$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.ba	$1$	$0$	\(0\)	\(5\)	\(9\)	\(3\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+\beta _{5}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
5720.2.a.bb	$5720$	$2$	5720.a	1.a	$1$	$10$	$10$	$45.674$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.bb	$1$	$0$	\(0\)	\(1\)	\(-10\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-\beta _{5}q^{7}+(2+\beta _{2})q^{9}+\cdots\)
5720.2.a.bc	$5720$	$2$	5720.a	1.a	$1$	$10$	$10$	$45.674$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	5720.2.a.bc	$1$	$0$	\(0\)	\(1\)	\(10\)	\(3\)		$-$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-\beta _{4}q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5720))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5720)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(715))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1430))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2860))\)\(^{\oplus 2}\)