Space of modular forms of level 1134, weight 2, and trivial character

• Label: 1134.2.a
• Level: $1134$
• Weight: $2$
• Character orbit: 1134.a
• Rep. character: $\chi_{1134}(1,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $16$
• Sturm bound: $432$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(432\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1134))\).

	Total	New	Old
Modular forms	240	24	216
Cusp forms	193	24	169
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.

\(2\)	\(3\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(25\)	\(2\)	\(23\)		\(20\)	\(2\)	\(18\)		\(5\)	\(0\)	\(5\)
\(+\)	\(+\)	\(-\)	\(-\)		\(35\)	\(4\)	\(31\)		\(29\)	\(4\)	\(25\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)		\(34\)	\(4\)	\(30\)		\(28\)	\(4\)	\(24\)		\(6\)	\(0\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)		\(26\)	\(2\)	\(24\)		\(20\)	\(2\)	\(18\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(+\)	\(-\)		\(29\)	\(3\)	\(26\)		\(23\)	\(3\)	\(20\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)	\(+\)		\(31\)	\(1\)	\(30\)		\(25\)	\(1\)	\(24\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)	\(+\)		\(32\)	\(3\)	\(29\)		\(26\)	\(3\)	\(23\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(-\)	\(-\)		\(28\)	\(5\)	\(23\)		\(22\)	\(5\)	\(17\)		\(6\)	\(0\)	\(6\)
Plus space			\(+\)		\(114\)	\(8\)	\(106\)		\(91\)	\(8\)	\(83\)		\(23\)	\(0\)	\(23\)
Minus space			\(-\)		\(126\)	\(16\)	\(110\)		\(102\)	\(16\)	\(86\)		\(24\)	\(0\)	\(24\)

Trace form

24 * q + 24 * q^4 - 12 * q^10 - 12 * q^13 + 24 * q^16 + 12 * q^19 + 12 * q^22 + 36 * q^25 + 24 * q^31 + 12 * q^37 - 12 * q^40 + 12 * q^43 + 24 * q^49 - 12 * q^52 + 24 * q^55 - 12 * q^58 - 12 * q^61 + 24 * q^64 + 36 * q^67 + 12 * q^76 + 24 * q^79 - 12 * q^82 - 12 * q^85 + 12 * q^88 + 24 * q^91 - 36 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\) 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	7
1134.2.a.a	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓				126.2.f.a	$1$	$0$	\(-1\)	\(0\)	\(-3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
1134.2.a.b	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓	✓			1134.2.a.b	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1134.2.a.c	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓				126.2.f.b	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
1134.2.a.d	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓	✓			1134.2.a.d	$1$	$0$	\(-1\)	\(0\)	\(3\)	\(1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1134.2.a.e	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓	✓	✓	✓	1134.2.a.d	$1$	$1$	\(1\)	\(0\)	\(-3\)	\(1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1134.2.a.f	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓				126.2.f.b	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1134.2.a.g	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓	✓			1134.2.a.b	$1$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1134.2.a.h	$1134$	$2$	1134.a	1.a	$1$	$1$	$1$	$9.055$	\(\Q\)	None	✓				126.2.f.a	$1$	$0$	\(1\)	\(0\)	\(3\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1134.2.a.i	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{6}) \)	None	✓				126.2.f.c	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1134.2.a.j	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	1134.2.a.j	$1$	$1$	\(-2\)	\(0\)	\(0\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1134.2.a.k	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{33}) \)	None	✓		✓		126.2.f.d	$1$	$0$	\(-2\)	\(0\)	\(3\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
1134.2.a.l	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{3}) \)	None	✓	✓			1134.2.a.l	$1$	$0$	\(-2\)	\(0\)	\(4\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1134.2.a.m	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓		1134.2.a.l	$1$	$1$	\(2\)	\(0\)	\(-4\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-2+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
1134.2.a.n	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{33}) \)	None	✓				126.2.f.d	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}+q^{8}+\cdots\)
1134.2.a.o	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{3}) \)	None	✓	✓			1134.2.a.j	$1$	$0$	\(2\)	\(0\)	\(0\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1134.2.a.p	$1134$	$2$	1134.a	1.a	$1$	$2$	$2$	$9.055$	\(\Q(\sqrt{6}) \)	None	✓		✓		126.2.f.c	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1134))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1134)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(567))\)\(^{\oplus 2}\)