Space of modular forms of level 6760, weight 2, and trivial character

• Label: 6760.2.a
• Level: $6760$
• Weight: $2$
• Character orbit: 6760.a
• Rep. character: $\chi_{6760}(1,\cdot)$
• Character field: $\Q$
• Dimension: $155$
• Newform subspaces: $42$
• Sturm bound: $2184$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 6760 = 2^{3} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6760.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 42 \)
Sturm bound:			\(2184\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6760))\).

	Total	New	Old
Modular forms	1148	155	993
Cusp forms	1037	155	882
Eisenstein series	111	0	111

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

\(2\)	\(5\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(18\)
\(+\)	\(+\)	\(-\)	$-$	\(21\)
\(+\)	\(-\)	\(+\)	$-$	\(24\)
\(+\)	\(-\)	\(-\)	$+$	\(15\)
\(-\)	\(+\)	\(+\)	$-$	\(17\)
\(-\)	\(+\)	\(-\)	$+$	\(21\)
\(-\)	\(-\)	\(+\)	$+$	\(18\)
\(-\)	\(-\)	\(-\)	$-$	\(21\)
Plus space			\(+\)	\(72\)
Minus space			\(-\)	\(83\)

Trace form

\( 155 q + 4 q^{3} + q^{5} + 4 q^{7} + 151 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6760))\) 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	13
6760.2.a.a	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}+3q^{7}+6q^{9}+5q^{11}+\cdots\)
6760.2.a.b	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+q^{5}-3q^{7}+6q^{9}-5q^{11}+\cdots\)
6760.2.a.c	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$2$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}-3q^{11}+\cdots\)
6760.2.a.d	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}-2q^{9}+q^{11}+q^{15}+\cdots\)
6760.2.a.e	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
6760.2.a.f	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-3q^{7}-2q^{9}+5q^{11}+\cdots\)
6760.2.a.g	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}-2q^{9}-q^{11}-q^{15}+\cdots\)
6760.2.a.h	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(3\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+3q^{7}-2q^{9}+3q^{11}+\cdots\)
6760.2.a.i	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+4q^{7}-3q^{9}-4q^{11}+2q^{17}+\cdots\)
6760.2.a.j	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}+4q^{11}-6q^{17}-4q^{19}+\cdots\)
6760.2.a.k	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
6760.2.a.l	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+3q^{7}+q^{9}-5q^{11}+\cdots\)
6760.2.a.m	$6760$	$2$	6760.a	1.a	$1$	$1$	$1$	$53.979$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(1\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
6760.2.a.n	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-2\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta )q^{3}-q^{5}+2q^{7}+(3-4\beta )q^{9}+\cdots\)
6760.2.a.o	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
6760.2.a.p	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
6760.2.a.q	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}-q^{7}+(1+\beta )q^{9}+3q^{11}+\cdots\)
6760.2.a.r	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+q^{7}+(1+\beta )q^{9}-3q^{11}+\cdots\)
6760.2.a.s	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(2-\beta )q^{11}+\cdots\)
6760.2.a.t	$6760$	$2$	6760.a	1.a	$1$	$2$	$2$	$53.979$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(2\)	\(2\)	\(0\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+q^{5}+(3+2\beta )q^{9}+(-3+\cdots)q^{11}+\cdots\)
6760.2.a.u	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
6760.2.a.v	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(3\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.w	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(9\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6760.2.a.x	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	3.3.1016.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-9\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-3q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
6760.2.a.y	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{3}-q^{5}+\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
6760.2.a.z	$6760$	$2$	6760.a	1.a	$1$	$3$	$3$	$53.979$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1}-\beta _{2})q^{3}+q^{5}-\beta _{2}q^{7}+(3+\cdots)q^{9}+\cdots\)
6760.2.a.ba	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.25488.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+(1+\beta _{1}+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bb	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.25488.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+(-1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
6760.2.a.bc	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.34868.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(-4\)	\(-6\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}-\beta _{3})q^{7}+\cdots\)
6760.2.a.bd	$6760$	$2$	6760.a	1.a	$1$	$4$	$4$	$53.979$	4.4.34868.1	None	✓	$1$	$0$	\(0\)	\(2\)	\(4\)	\(6\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
6760.2.a.be	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.406193977.1	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{5}-\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
6760.2.a.bf	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.406193977.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(6\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}+q^{5}+\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
6760.2.a.bg	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.7674048.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(-6\)	\(-4\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}+\beta _{4}-\beta _{5})q^{7}+\cdots\)
6760.2.a.bh	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.2249737.1	None	✓	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}-q^{5}-\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bi	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.2249737.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(6\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{3}+q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bj	$6760$	$2$	6760.a	1.a	$1$	$6$	$6$	$53.979$	6.6.7674048.1	None	✓	$1$	$1$	\(0\)	\(0\)	\(6\)	\(4\)		$+$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{4}+\beta _{5})q^{7}+\cdots\)
6760.2.a.bk	$6760$	$2$	6760.a	1.a	$1$	$8$	$8$	$53.979$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(-8\)	\(-6\)		$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1+\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.bl	$6760$	$2$	6760.a	1.a	$1$	$8$	$8$	$53.979$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(4\)	\(8\)	\(6\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1-\beta _{5})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
6760.2.a.bm	$6760$	$2$	6760.a	1.a	$1$	$9$	$9$	$53.979$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-9\)	\(7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}+(1-\beta _{2}+\beta _{8})q^{7}+(1+\cdots)q^{9}+\cdots\)
6760.2.a.bn	$6760$	$2$	6760.a	1.a	$1$	$9$	$9$	$53.979$	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(9\)	\(-7\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(-1+\beta _{2}-\beta _{8})q^{7}+\cdots\)
6760.2.a.bo	$6760$	$2$	6760.a	1.a	$1$	$12$	$12$	$53.979$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(-12\)	\(-7\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(-1-\beta _{10})q^{7}+(2+\cdots)q^{9}+\cdots\)
6760.2.a.bp	$6760$	$2$	6760.a	1.a	$1$	$12$	$12$	$53.979$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(12\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(1+\beta _{10})q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3380))\)\(^{\oplus 2}\)