Space of modular forms of level 2760, weight 2, and trivial character

• Label: 2760.2.a
• Level: $2760$
• Weight: $2$
• Character orbit: 2760.a
• Rep. character: $\chi_{2760}(1,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $23$
• Sturm bound: $1152$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2760.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(1152\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2760))\).

	Total	New	Old
Modular forms	592	44	548
Cusp forms	561	44	517
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.

\(2\)	\(3\)	\(5\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(3\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(3\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(1\)
Plus space				\(+\)	\(18\)
Minus space				\(-\)	\(26\)

Trace form

\( 44 q - 4 q^{3} - 8 q^{7} + 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2760))\) 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	5	23
2760.2.a.a	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2760.2.a.b	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(3\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
2760.2.a.c	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.c	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
2760.2.a.d	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
2760.2.a.e	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(0\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2760.2.a.f	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓	✓	✓	2760.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(1\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
2760.2.a.g	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.g	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
2760.2.a.h	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.h	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots\)
2760.2.a.i	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.i	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(3\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+3q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
2760.2.a.j	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓	✓	✓	2760.2.a.j	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-3\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-3q^{7}+q^{9}-4q^{11}+q^{15}+\cdots\)
2760.2.a.k	$2760$	$2$	2760.a	1.a	$1$	$1$	$1$	$22.039$	\(\Q\)	None	✓	✓			2760.2.a.k	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}+2q^{11}+q^{15}+6q^{17}+\cdots\)
2760.2.a.l	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	\(\Q(\sqrt{11}) \)	None	✓	✓	✓		2760.2.a.l	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(-6\)		$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-3q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
2760.2.a.m	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	2760.2.a.m	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-3\)		$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
2760.2.a.n	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓		2760.2.a.n	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
2760.2.a.o	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	\(\Q(\sqrt{33}) \)	None	✓	✓	✓		2760.2.a.o	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(1\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+\beta q^{7}+q^{9}+4q^{11}+(-2+\cdots)q^{13}+\cdots\)
2760.2.a.p	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	2760.2.a.p	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-1\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
2760.2.a.q	$2760$	$2$	2760.a	1.a	$1$	$2$	$2$	$22.039$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	2760.2.a.q	$1$	$1$	\(0\)	\(2\)	\(2\)	\(-2\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}+q^{9}+(-2+3\beta )q^{11}+\cdots\)
2760.2.a.r	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.316.1	None	✓	✓	✓	✓	2760.2.a.r	$1$	$1$	\(0\)	\(3\)	\(-3\)	\(-6\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-2+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2760.2.a.s	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.1436.1	None	✓	✓	✓	✓	2760.2.a.s	$1$	$0$	\(0\)	\(3\)	\(-3\)	\(-2\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1+\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2760.2.a.t	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.229.1	None	✓	✓	✓	✓	2760.2.a.t	$1$	$0$	\(0\)	\(3\)	\(3\)	\(1\)		$+$	$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(1-\beta _{2})q^{13}+\cdots\)
2760.2.a.u	$2760$	$2$	2760.a	1.a	$1$	$3$	$3$	$22.039$	3.3.568.1	None	✓	✓	✓		2760.2.a.u	$1$	$0$	\(0\)	\(3\)	\(3\)	\(2\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1-2\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
2760.2.a.v	$2760$	$2$	2760.a	1.a	$1$	$4$	$4$	$22.039$	4.4.54764.1	None	✓	✓	✓	✓	2760.2.a.v	$1$	$1$	\(0\)	\(-4\)	\(-4\)	\(0\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
2760.2.a.w	$2760$	$2$	2760.a	1.a	$1$	$5$	$5$	$22.039$	5.5.20087896.1	None	✓	✓	✓	✓	2760.2.a.w	$1$	$0$	\(0\)	\(-5\)	\(5\)	\(-4\)		$+$	$+$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2760)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 2}\)