Space of modular forms of level 1080, weight 2, and trivial character

• Label: 1080.2.a
• Level: $1080$
• Weight: $2$
• Character orbit: 1080.a
• Rep. character: $\chi_{1080}(1,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $14$
• Sturm bound: $432$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1080.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(432\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1080))\).

	Total	New	Old
Modular forms	240	16	224
Cusp forms	193	16	177
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.

\(2\)	\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(24\)	\(1\)	\(23\)		\(19\)	\(1\)	\(18\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(33\)	\(2\)	\(31\)		\(27\)	\(2\)	\(25\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(36\)	\(3\)	\(33\)		\(30\)	\(3\)	\(27\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(27\)	\(2\)	\(25\)		\(21\)	\(2\)	\(19\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(30\)	\(2\)	\(28\)		\(24\)	\(2\)	\(22\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(33\)	\(1\)	\(32\)		\(27\)	\(1\)	\(26\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(30\)	\(2\)	\(28\)		\(24\)	\(2\)	\(22\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(27\)	\(3\)	\(24\)		\(21\)	\(3\)	\(18\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(114\)	\(6\)	\(108\)		\(91\)	\(6\)	\(85\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(126\)	\(10\)	\(116\)		\(102\)	\(10\)	\(92\)		\(24\)	\(0\)	\(24\)

Trace form

\( 16 q - 4 q^{7} - 4 q^{13} - 4 q^{19} + 16 q^{25} + 36 q^{31} + 4 q^{37} + 40 q^{43} + 20 q^{49} + 4 q^{55} + 4 q^{61} + 4 q^{67} + 4 q^{73} + 8 q^{79} + 4 q^{91} + 12 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\) 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
1080.2.a.a	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-4q^{7}+2q^{11}+4q^{13}+q^{17}+\cdots\)
1080.2.a.b	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{7}-6q^{13}+7q^{17}+7q^{19}+\cdots\)
1080.2.a.c	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-q^{7}+2q^{11}-5q^{13}+4q^{17}+\cdots\)
1080.2.a.d	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓	✓	✓	1080.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-2q^{11}-3q^{17}-q^{19}-3q^{23}+\cdots\)
1080.2.a.e	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.e	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-4q^{11}-2q^{13}-5q^{17}+\cdots\)
1080.2.a.f	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.f	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-q^{11}+q^{13}+q^{17}+\cdots\)
1080.2.a.g	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-4q^{7}-2q^{11}+4q^{13}-q^{17}+\cdots\)
1080.2.a.h	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓	✓	✓	1080.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{7}-6q^{13}-7q^{17}+7q^{19}+\cdots\)
1080.2.a.i	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.c	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-q^{7}-2q^{11}-5q^{13}-4q^{17}+\cdots\)
1080.2.a.j	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.d	$1$	$0$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{11}+3q^{17}-q^{19}+3q^{23}+\cdots\)
1080.2.a.k	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.f	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+q^{11}+q^{13}-q^{17}+\cdots\)
1080.2.a.l	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	\(\Q\)	None	✓	✓			1080.2.a.e	$1$	$0$	\(0\)	\(0\)	\(1\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}+4q^{11}-2q^{13}+5q^{17}+\cdots\)
1080.2.a.m	$1080$	$2$	1080.a	1.a	$1$	$2$	$2$	$8.624$	\(\Q(\sqrt{73}) \)	None	✓	✓	✓		1080.2.a.m	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(1\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+\beta q^{7}+(1-\beta )q^{11}+3q^{13}+\cdots\)
1080.2.a.n	$1080$	$2$	1080.a	1.a	$1$	$2$	$2$	$8.624$	\(\Q(\sqrt{73}) \)	None	✓	✓	✓		1080.2.a.m	$1$	$0$	\(0\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}+3q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1080)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 2}\)