Space of modular forms of level 1920, weight 2, and trivial character

• Label: 1920.2.a
• Level: $1920$
• Weight: $2$
• Character orbit: 1920.a
• Rep. character: $\chi_{1920}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $28$
• Sturm bound: $768$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 28 \)
Sturm bound:			\(768\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1920))\).

	Total	New	Old
Modular forms	416	32	384
Cusp forms	353	32	321
Eisenstein series	63	0	63

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	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)	\(6\)
Plus space			\(+\)	\(12\)
Minus space			\(-\)	\(20\)

Trace form

\( 32 q + 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\) 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
1920.2.a.a	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}+q^{15}+\cdots\)
1920.2.a.b	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1920.2.a.c	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1920.2.a.d	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(0\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
1920.2.a.e	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
1920.2.a.f	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.f	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+4q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
1920.2.a.g	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.f	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
1920.2.a.h	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1920.2.a.i	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.d	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
1920.2.a.j	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
1920.2.a.k	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
1920.2.a.l	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(1\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+4q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
1920.2.a.m	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-4q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
1920.2.a.n	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
1920.2.a.o	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.d	$1$	$1$	\(0\)	\(1\)	\(-1\)	\(0\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
1920.2.a.p	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1920.2.a.q	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+2q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1920.2.a.r	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+4q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
1920.2.a.s	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.a	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-4\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+q^{15}+\cdots\)
1920.2.a.t	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-6q^{13}+\cdots\)
1920.2.a.u	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.b	$1$	$0$	\(0\)	\(1\)	\(1\)	\(-2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-2q^{7}+q^{9}+6q^{11}+2q^{13}+\cdots\)
1920.2.a.v	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.d	$1$	$0$	\(0\)	\(1\)	\(1\)	\(0\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
1920.2.a.w	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.e	$1$	$0$	\(0\)	\(1\)	\(1\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1920.2.a.x	$1920$	$2$	1920.a	1.a	$1$	$1$	$1$	$15.331$	\(\Q\)	None	✓	✓			1920.2.a.f	$1$	$0$	\(0\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}-4q^{13}+\cdots\)
1920.2.a.y	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		1920.2.a.y	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
1920.2.a.z	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		1920.2.a.y	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
1920.2.a.ba	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		1920.2.a.y	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+2q^{11}+\cdots\)
1920.2.a.bb	$1920$	$2$	1920.a	1.a	$1$	$2$	$2$	$15.331$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓		1920.2.a.y	$1$	$0$	\(0\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1920)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 2}\)