Space of modular forms of level 1160, weight 2, and trivial character

• Label: 1160.2.a
• Level: $1160$
• Weight: $2$
• Character orbit: 1160.a
• Rep. character: $\chi_{1160}(1,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $10$
• Sturm bound: $360$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1160.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(360\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1160))\).

	Total	New	Old
Modular forms	188	28	160
Cusp forms	173	28	145
Eisenstein series	15	0	15

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
\(+\)	\(+\)	\(+\)	\(+\)		\(21\)	\(2\)	\(19\)		\(20\)	\(2\)	\(18\)		\(1\)	\(0\)	\(1\)
\(+\)	\(+\)	\(-\)	\(-\)		\(26\)	\(5\)	\(21\)		\(24\)	\(5\)	\(19\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(+\)	\(-\)		\(26\)	\(5\)	\(21\)		\(24\)	\(5\)	\(19\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)		\(21\)	\(1\)	\(20\)		\(19\)	\(1\)	\(18\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)		\(26\)	\(4\)	\(22\)		\(24\)	\(4\)	\(20\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)	\(+\)		\(21\)	\(3\)	\(18\)		\(19\)	\(3\)	\(16\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)		\(21\)	\(3\)	\(18\)		\(19\)	\(3\)	\(16\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(-\)	\(-\)		\(26\)	\(5\)	\(21\)		\(24\)	\(5\)	\(19\)		\(2\)	\(0\)	\(2\)
Plus space			\(+\)		\(84\)	\(9\)	\(75\)		\(77\)	\(9\)	\(68\)		\(7\)	\(0\)	\(7\)
Minus space			\(-\)		\(104\)	\(19\)	\(85\)		\(96\)	\(19\)	\(77\)		\(8\)	\(0\)	\(8\)

Trace form

28 * q + 8 * q^7 + 40 * q^9 - 8 * q^11 + 8 * q^13 + 4 * q^17 - 8 * q^19 - 8 * q^21 + 28 * q^25 + 32 * q^31 + 8 * q^33 - 4 * q^35 + 4 * q^37 + 8 * q^39 + 16 * q^41 + 32 * q^43 + 24 * q^47 + 48 * q^49 - 8 * q^51 - 24 * q^53 + 32 * q^57 + 12 * q^59 + 8 * q^61 + 32 * q^63 + 12 * q^65 - 8 * q^67 + 48 * q^69 - 8 * q^71 + 28 * q^73 + 16 * q^77 + 24 * q^79 + 28 * q^81 - 8 * q^83 - 4 * q^85 + 16 * q^91 + 24 * q^93 - 8 * q^95 + 36 * q^97 - 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1160))\) 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
1160.2.a.a	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	\(\Q\)	None	✓	✓			1160.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(-1\)	\(0\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
1160.2.a.b	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	\(\Q\)	None	✓	✓	✓	✓	1160.2.a.b	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-3q^{9}-2q^{13}-6q^{17}-8q^{19}+\cdots\)
1160.2.a.c	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	\(\Q\)	None	✓	✓			1160.2.a.c	$1$	$1$	\(0\)	\(2\)	\(-1\)	\(-4\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\)
1160.2.a.d	$1160$	$2$	1160.a	1.a	$1$	$1$	$1$	$9.263$	\(\Q\)	None	✓	✓			1160.2.a.d	$1$	$0$	\(0\)	\(2\)	\(-1\)	\(4\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}-q^{5}+4q^{7}+q^{9}+6q^{13}+\cdots\)
1160.2.a.e	$1160$	$2$	1160.a	1.a	$1$	$3$	$3$	$9.263$	3.3.148.1	None	✓	✓	✓	✓	1160.2.a.e	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(2\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-q^{5}+(1-\beta _{2})q^{7}+\cdots\)
1160.2.a.f	$1160$	$2$	1160.a	1.a	$1$	$3$	$3$	$9.263$	3.3.148.1	None	✓	✓	✓	✓	1160.2.a.f	$1$	$1$	\(0\)	\(-2\)	\(3\)	\(-4\)		$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
1160.2.a.g	$1160$	$2$	1160.a	1.a	$1$	$3$	$3$	$9.263$	3.3.229.1	None	✓	✓	✓		1160.2.a.g	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1160.2.a.h	$1160$	$2$	1160.a	1.a	$1$	$5$	$5$	$9.263$	5.5.3145252.1	None	✓	✓	✓	✓	1160.2.a.h	$1$	$0$	\(0\)	\(-1\)	\(-5\)	\(7\)		$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{3}q^{3}-q^{5}+(1-\beta _{2})q^{7}+(2-\beta _{2}+\cdots)q^{9}+\cdots\)
1160.2.a.i	$1160$	$2$	1160.a	1.a	$1$	$5$	$5$	$9.263$	5.5.6083172.1	None	✓	✓	✓	✓	1160.2.a.i	$1$	$0$	\(0\)	\(-1\)	\(5\)	\(-1\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
1160.2.a.j	$1160$	$2$	1160.a	1.a	$1$	$5$	$5$	$9.263$	5.5.580484.1	None	✓	✓	✓	✓	1160.2.a.j	$1$	$0$	\(0\)	\(3\)	\(5\)	\(7\)		$-$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	\(q+(1-\beta _{3})q^{3}+q^{5}+(1-\beta _{2}+\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1160))\) into lower level spaces

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