Space of modular forms of level 945, weight 2, and trivial character

• Label: 945.2.a
• Level: $945$
• Weight: $2$
• Character orbit: 945.a
• Rep. character: $\chi_{945}(1,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $14$
• Sturm bound: $288$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(288\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(945))\).

	Total	New	Old
Modular forms	156	32	124
Cusp forms	133	32	101
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.

\(3\)	\(5\)	\(7\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(15\)	\(4\)	\(11\)		\(13\)	\(4\)	\(9\)		\(2\)	\(0\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)		\(23\)	\(6\)	\(17\)		\(20\)	\(6\)	\(14\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)		\(21\)	\(4\)	\(17\)		\(18\)	\(4\)	\(14\)		\(3\)	\(0\)	\(3\)
\(+\)	\(-\)	\(-\)	\(+\)		\(19\)	\(2\)	\(17\)		\(16\)	\(2\)	\(14\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)		\(21\)	\(4\)	\(17\)		\(18\)	\(4\)	\(14\)		\(3\)	\(0\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)		\(17\)	\(2\)	\(15\)		\(14\)	\(2\)	\(12\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)		\(21\)	\(4\)	\(17\)		\(18\)	\(4\)	\(14\)		\(3\)	\(0\)	\(3\)
\(-\)	\(-\)	\(-\)	\(-\)		\(19\)	\(6\)	\(13\)		\(16\)	\(6\)	\(10\)		\(3\)	\(0\)	\(3\)
Plus space			\(+\)		\(72\)	\(12\)	\(60\)		\(61\)	\(12\)	\(49\)		\(11\)	\(0\)	\(11\)
Minus space			\(-\)		\(84\)	\(20\)	\(64\)		\(72\)	\(20\)	\(52\)		\(12\)	\(0\)	\(12\)

Trace form

32 * q + 28 * q^4 - 4 * q^10 + 52 * q^16 - 8 * q^19 + 32 * q^22 + 32 * q^25 + 32 * q^28 - 24 * q^31 + 20 * q^34 - 8 * q^37 + 24 * q^40 - 16 * q^43 + 12 * q^46 + 32 * q^49 - 32 * q^52 - 8 * q^55 - 24 * q^58 - 40 * q^61 + 104 * q^64 + 48 * q^67 - 32 * q^73 - 60 * q^76 + 24 * q^79 - 72 * q^82 - 16 * q^85 + 24 * q^88 - 8 * q^91 - 48 * q^94 + 40 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(945))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5	7
945.2.a.a	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	945.2.a.a	$1$	$1$	\(-3\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{2}+3\beta q^{4}+q^{5}+q^{7}+\cdots\)
945.2.a.b	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{2}) \)	None	✓	✓			945.2.a.b	$1$	$0$	\(-2\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-q^{5}-q^{7}+\cdots\)
945.2.a.c	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.c	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.d	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.d	$1$	$1$	\(-1\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.e	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.e	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+q^{5}-q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.f	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{13}) \)	None	✓	✓	✓	✓	945.2.a.f	$1$	$1$	\(-1\)	\(0\)	\(-2\)	\(2\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots\)
945.2.a.g	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.e	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.h	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.c	$1$	$1$	\(1\)	\(0\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.i	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.d	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+\beta )q^{4}-q^{5}-q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.j	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{13}) \)	None	✓	✓			945.2.a.f	$1$	$0$	\(1\)	\(0\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(1+\beta )q^{4}+q^{5}+q^{7}+3q^{8}+\cdots\)
945.2.a.k	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{2}) \)	None	✓	✓			945.2.a.b	$1$	$0$	\(2\)	\(0\)	\(2\)	\(-2\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}-q^{7}+\cdots\)
945.2.a.l	$945$	$2$	945.a	1.a	$1$	$2$	$2$	$7.546$	\(\Q(\sqrt{5}) \)	None	✓	✓			945.2.a.a	$1$	$0$	\(3\)	\(0\)	\(-2\)	\(2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+3\beta q^{4}-q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)
945.2.a.m	$945$	$2$	945.a	1.a	$1$	$4$	$4$	$7.546$	4.4.144344.1	None	✓	✓	✓		945.2.a.m	$1$	$0$	\(-1\)	\(0\)	\(-4\)	\(4\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+q^{7}+(-1+\cdots)q^{8}+\cdots\)
945.2.a.n	$945$	$2$	945.a	1.a	$1$	$4$	$4$	$7.546$	4.4.144344.1	None	✓	✓	✓		945.2.a.m	$1$	$0$	\(1\)	\(0\)	\(4\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+q^{7}+(1+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(945))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(945)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 2}\)