Space of modular forms of level 7120, weight 2, and trivial character

• Label: 7120.2.a
• Level: $7120$
• Weight: $2$
• Character orbit: 7120.a
• Rep. character: $\chi_{7120}(1,\cdot)$
• Character field: $\Q$
• Dimension: $176$
• Newform subspaces: $44$
• Sturm bound: $2160$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 7120 = 2^{4} \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7120.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 44 \)
Sturm bound:			\(2160\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7120))\).

	Total	New	Old
Modular forms	1092	176	916
Cusp forms	1069	176	893
Eisenstein series	23	0	23

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

\(2\)	\(5\)	\(89\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(21\)
\(+\)	\(+\)	\(-\)	$-$	\(23\)
\(+\)	\(-\)	\(+\)	$-$	\(23\)
\(+\)	\(-\)	\(-\)	$+$	\(21\)
\(-\)	\(+\)	\(+\)	$-$	\(23\)
\(-\)	\(+\)	\(-\)	$+$	\(21\)
\(-\)	\(-\)	\(+\)	$+$	\(21\)
\(-\)	\(-\)	\(-\)	$-$	\(23\)
Plus space			\(+\)	\(84\)
Minus space			\(-\)	\(92\)

Trace form

\( 176 q - 4 q^{3} - 4 q^{7} + 176 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7120))\) 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	5	89
7120.2.a.a	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-4q^{7}+q^{9}+2q^{15}+\cdots\)
7120.2.a.b	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
7120.2.a.c	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
7120.2.a.d	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}-2q^{9}+5q^{11}+\cdots\)
7120.2.a.e	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots\)
7120.2.a.f	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}-3q^{9}+2q^{17}+6q^{19}+\cdots\)
7120.2.a.g	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(0\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
7120.2.a.h	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{13}+2q^{17}-2q^{19}+\cdots\)
7120.2.a.i	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-3q^{9}+4q^{11}+6q^{13}+\cdots\)
7120.2.a.j	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots\)
7120.2.a.k	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
7120.2.a.l	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
7120.2.a.m	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
7120.2.a.n	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
7120.2.a.o	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
7120.2.a.p	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
7120.2.a.q	$7120$	$2$	7120.a	1.a	$1$	$1$	$1$	$56.853$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}-q^{5}+6q^{9}-3q^{11}-4q^{13}+\cdots\)
7120.2.a.r	$7120$	$2$	7120.a	1.a	$1$	$2$	$2$	$56.853$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7120.2.a.s	$7120$	$2$	7120.a	1.a	$1$	$2$	$2$	$56.853$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7120.2.a.t	$7120$	$2$	7120.a	1.a	$1$	$2$	$2$	$56.853$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+(3+\beta )q^{7}-3q^{9}-2\beta q^{11}+\cdots\)
7120.2.a.u	$7120$	$2$	7120.a	1.a	$1$	$2$	$2$	$56.853$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+q^{5}-\beta q^{7}-q^{9}-4q^{11}+\cdots\)
7120.2.a.v	$7120$	$2$	7120.a	1.a	$1$	$2$	$2$	$56.853$	\(\Q(\sqrt{33}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}+2q^{7}+(5+\beta )q^{9}+(4+\cdots)q^{11}+\cdots\)
7120.2.a.w	$7120$	$2$	7120.a	1.a	$1$	$2$	$2$	$56.853$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}-q^{5}+(-1-\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
7120.2.a.x	$7120$	$2$	7120.a	1.a	$1$	$3$	$3$	$56.853$	3.3.404.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7120.2.a.y	$7120$	$2$	7120.a	1.a	$1$	$3$	$3$	$56.853$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(3\)	\(-2\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(-1+\beta _{1})q^{7}+\cdots\)
7120.2.a.z	$7120$	$2$	7120.a	1.a	$1$	$4$	$4$	$56.853$	4.4.8069.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(4\)	\(-12\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1}-\beta _{3})q^{3}+q^{5}-3q^{7}+\cdots\)
7120.2.a.ba	$7120$	$2$	7120.a	1.a	$1$	$4$	$4$	$56.853$	4.4.3981.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+(1-2\beta _{1})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
7120.2.a.bb	$7120$	$2$	7120.a	1.a	$1$	$4$	$4$	$56.853$	4.4.9909.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(4\)	\(4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+q^{7}+(\beta _{1}+\beta _{2})q^{9}+\cdots\)
7120.2.a.bc	$7120$	$2$	7120.a	1.a	$1$	$4$	$4$	$56.853$	4.4.725.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+(-1+2\beta _{1})q^{7}+(-1+\cdots)q^{9}+\cdots\)
7120.2.a.bd	$7120$	$2$	7120.a	1.a	$1$	$5$	$5$	$56.853$	5.5.1186628.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-5\)	\(-8\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-q^{5}+(-1-\beta _{3}-\beta _{4})q^{7}+\cdots\)
7120.2.a.be	$7120$	$2$	7120.a	1.a	$1$	$5$	$5$	$56.853$	5.5.7736352.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{3}q^{7}+(2+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
7120.2.a.bf	$7120$	$2$	7120.a	1.a	$1$	$6$	$6$	$56.853$	6.6.387230992.1	None	✓	$1$	$1$	\(0\)	\(-3\)	\(6\)	\(-6\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{3}-\beta _{5})q^{7}+\cdots\)
7120.2.a.bg	$7120$	$2$	7120.a	1.a	$1$	$6$	$6$	$56.853$	6.6.95127372.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(-6\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}-q^{5}+\beta _{1}q^{7}+(2-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7120.2.a.bh	$7120$	$2$	7120.a	1.a	$1$	$6$	$6$	$56.853$	6.6.363514872.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(6\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{1}+\beta _{5})q^{7}+\cdots\)
7120.2.a.bi	$7120$	$2$	7120.a	1.a	$1$	$6$	$6$	$56.853$	6.6.5431612.1	None	✓	$1$	$1$	\(0\)	\(2\)	\(6\)	\(4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{4}q^{3}+q^{5}+(1+\beta _{3}+\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots\)
7120.2.a.bj	$7120$	$2$	7120.a	1.a	$1$	$7$	$7$	$56.853$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(8\)	\(7\)	\(16\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta _{5})q^{3}+q^{5}+(2+\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
7120.2.a.bk	$7120$	$2$	7120.a	1.a	$1$	$8$	$8$	$56.853$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-8\)	\(6\)		$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{4})q^{3}-q^{5}+(1-\beta _{5}-\beta _{7})q^{7}+\cdots\)
7120.2.a.bl	$7120$	$2$	7120.a	1.a	$1$	$8$	$8$	$56.853$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-8\)	\(-2\)		$-$	$+$	$+$	$-$	$2^{2}\cdot 3$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+\beta _{4}q^{7}+(1-\beta _{2}-\beta _{5}+\cdots)q^{9}+\cdots\)
7120.2.a.bm	$7120$	$2$	7120.a	1.a	$1$	$9$	$9$	$56.853$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(9\)	\(8\)		$+$	$-$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{6})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
7120.2.a.bn	$7120$	$2$	7120.a	1.a	$1$	$10$	$10$	$56.853$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-10\)	\(-10\)		$+$	$+$	$+$	$+$	$2^{4}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{2})q^{7}+(1-\beta _{6}+\cdots)q^{9}+\cdots\)
7120.2.a.bo	$7120$	$2$	7120.a	1.a	$1$	$11$	$11$	$56.853$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-11\)	\(12\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{9})q^{7}+(1+\beta _{8}+\cdots)q^{9}+\cdots\)
7120.2.a.bp	$7120$	$2$	7120.a	1.a	$1$	$12$	$12$	$56.853$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-7\)	\(12\)	\(-10\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{11})q^{7}+\cdots\)
7120.2.a.bq	$7120$	$2$	7120.a	1.a	$1$	$12$	$12$	$56.853$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-5\)	\(-12\)	\(-2\)		$+$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}-\beta _{6}q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7120.2.a.br	$7120$	$2$	7120.a	1.a	$1$	$14$	$14$	$56.853$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(14\)	\(-4\)		$+$	$-$	$+$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{8}q^{7}+(2+\beta _{2})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7120))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7120)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(356))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(445))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(712))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(890))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1424))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1780))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3560))\)\(^{\oplus 2}\)