Space of modular forms of level 2320, weight 2, and trivial character

• Label: 2320.2.a
• Level: $2320$
• Weight: $2$
• Character orbit: 2320.a
• Rep. character: $\chi_{2320}(1,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $23$
• Sturm bound: $720$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2320 = 2^{4} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2320.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 23 \)
Sturm bound:			\(720\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2320))\).

	Total	New	Old
Modular forms	372	56	316
Cusp forms	349	56	293
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.

\(2\)	\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(40\)	\(6\)	\(34\)		\(38\)	\(6\)	\(32\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(50\)	\(8\)	\(42\)		\(47\)	\(8\)	\(39\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(46\)	\(8\)	\(38\)		\(43\)	\(8\)	\(35\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(48\)	\(6\)	\(42\)		\(45\)	\(6\)	\(39\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(53\)	\(8\)	\(45\)		\(50\)	\(8\)	\(42\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(43\)	\(6\)	\(37\)		\(40\)	\(6\)	\(34\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(47\)	\(6\)	\(41\)		\(44\)	\(6\)	\(38\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(45\)	\(8\)	\(37\)		\(42\)	\(8\)	\(34\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(178\)	\(24\)	\(154\)		\(167\)	\(24\)	\(143\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(194\)	\(32\)	\(162\)		\(182\)	\(32\)	\(150\)		\(12\)	\(0\)	\(12\)

Trace form

56 * q - 4 * q^3 - 8 * q^7 + 64 * q^9 + 4 * q^15 + 8 * q^17 + 56 * q^25 - 16 * q^27 - 24 * q^31 - 8 * q^39 - 44 * q^43 - 4 * q^47 + 48 * q^49 + 48 * q^51 + 8 * q^55 - 16 * q^57 - 8 * q^59 - 16 * q^61 + 8 * q^63 + 8 * q^65 - 8 * q^67 + 16 * q^69 + 16 * q^71 + 8 * q^73 - 4 * q^75 + 32 * q^77 - 24 * q^79 + 72 * q^81 + 40 * q^83 - 16 * q^85 + 12 * q^87 + 16 * q^89 + 32 * q^93 + 16 * q^95 + 8 * q^97 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2320))\) 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	5	29
2320.2.a.a	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				1160.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}-4q^{7}+q^{9}+6q^{13}+\cdots\)
2320.2.a.b	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				1160.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+4q^{7}+q^{9}-2q^{13}+\cdots\)
2320.2.a.c	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				580.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-1\)	\(0\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}-3q^{9}+2q^{11}-2q^{13}+2q^{19}+\cdots\)
2320.2.a.d	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				290.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}-2q^{11}-6q^{13}+\cdots\)
2320.2.a.e	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				145.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{7}-3q^{9}+6q^{11}+2q^{13}+\cdots\)
2320.2.a.f	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				1160.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-2q^{13}-6q^{17}+8q^{19}+\cdots\)
2320.2.a.g	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				580.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}+2q^{7}-3q^{9}+4q^{11}-6q^{13}+\cdots\)
2320.2.a.h	$2320$	$2$	2320.a	1.a	$1$	$1$	$1$	$18.525$	\(\Q\)	None	✓				1160.2.a.a	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2320.2.a.i	$2320$	$2$	2320.a	1.a	$1$	$2$	$2$	$18.525$	\(\Q(\sqrt{13}) \)	None	✓				290.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-q^{5}+(-3+\beta )q^{7}+\beta q^{9}+\cdots\)
2320.2.a.j	$2320$	$2$	2320.a	1.a	$1$	$2$	$2$	$18.525$	\(\Q(\sqrt{13}) \)	None	✓				290.2.a.c	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(-3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+q^{5}+(-1-\beta )q^{7}+\beta q^{9}+\cdots\)
2320.2.a.k	$2320$	$2$	2320.a	1.a	$1$	$2$	$2$	$18.525$	\(\Q(\sqrt{2}) \)	None	✓				145.2.a.b	$1$	$0$	\(0\)	\(4\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+(2-\beta )q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
2320.2.a.l	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.621.1	None	✓				290.2.a.e	$1$	$0$	\(0\)	\(-3\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2320.2.a.m	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.564.1	None	✓				580.2.a.c	$1$	$0$	\(0\)	\(-2\)	\(-3\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots\)
2320.2.a.n	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	None	✓		✓		145.2.a.c	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
2320.2.a.o	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	None	✓				580.2.a.d	$1$	$0$	\(0\)	\(-2\)	\(3\)	\(-2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2320.2.a.p	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.229.1	None	✓		✓		1160.2.a.g	$1$	$1$	\(0\)	\(-1\)	\(-3\)	\(3\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}-q^{5}+(1-\beta _{1})q^{7}+(\beta _{1}-2\beta _{2})q^{9}+\cdots\)
2320.2.a.q	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.469.1	None	✓				290.2.a.d	$1$	$0$	\(0\)	\(1\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1+\beta _{1}-2\beta _{2})q^{9}+\cdots\)
2320.2.a.r	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	None	✓				1160.2.a.e	$1$	$0$	\(0\)	\(2\)	\(-3\)	\(-2\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2320.2.a.s	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	None	✓		✓		145.2.a.d	$1$	$1$	\(0\)	\(2\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
2320.2.a.t	$2320$	$2$	2320.a	1.a	$1$	$3$	$3$	$18.525$	3.3.148.1	None	✓				1160.2.a.f	$1$	$0$	\(0\)	\(2\)	\(3\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
2320.2.a.u	$2320$	$2$	2320.a	1.a	$1$	$5$	$5$	$18.525$	5.5.580484.1	None	✓		✓		1160.2.a.j	$1$	$1$	\(0\)	\(-3\)	\(5\)	\(-7\)		$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{3}+q^{5}+(-1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2320.2.a.v	$2320$	$2$	2320.a	1.a	$1$	$5$	$5$	$18.525$	5.5.3145252.1	None	✓		✓		1160.2.a.h	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(-7\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{3}q^{3}-q^{5}+(-1+\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
2320.2.a.w	$2320$	$2$	2320.a	1.a	$1$	$5$	$5$	$18.525$	5.5.6083172.1	None	✓		✓		1160.2.a.i	$1$	$0$	\(0\)	\(1\)	\(5\)	\(1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(\beta _{2}-\beta _{3})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2320)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1160))\)\(^{\oplus 2}\)