Space of modular forms of level 1944, weight 2, and trivial character

• Label: 1944.2.a
• Level: $1944$
• Weight: $2$
• Character orbit: 1944.a
• Rep. character: $\chi_{1944}(1,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $18$
• Sturm bound: $648$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1944.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(648\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1944))\).

	Total	New	Old
Modular forms	360	36	324
Cusp forms	289	36	253
Eisenstein series	71	0	71

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(85\)	\(9\)	\(76\)		\(68\)	\(9\)	\(59\)		\(17\)	\(0\)	\(17\)
\(+\)	\(-\)	\(-\)		\(94\)	\(9\)	\(85\)		\(76\)	\(9\)	\(67\)		\(18\)	\(0\)	\(18\)
\(-\)	\(+\)	\(-\)		\(95\)	\(12\)	\(83\)		\(77\)	\(12\)	\(65\)		\(18\)	\(0\)	\(18\)
\(-\)	\(-\)	\(+\)		\(86\)	\(6\)	\(80\)		\(68\)	\(6\)	\(62\)		\(18\)	\(0\)	\(18\)
Plus space		\(+\)		\(171\)	\(15\)	\(156\)		\(136\)	\(15\)	\(121\)		\(35\)	\(0\)	\(35\)
Minus space		\(-\)		\(189\)	\(21\)	\(168\)		\(153\)	\(21\)	\(132\)		\(36\)	\(0\)	\(36\)

Trace form

\( 36 q + 36 q^{25} + 18 q^{31} + 18 q^{43} + 36 q^{49} - 18 q^{55} - 18 q^{79} + 72 q^{85} + 18 q^{91} + 72 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1944))\) 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
1944.2.a.a	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+3q^{7}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
1944.2.a.b	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-3q^{7}-2q^{11}+q^{13}+8q^{17}+\cdots\)
1944.2.a.c	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.c	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}-2q^{11}+q^{13}+2q^{17}+5q^{19}+\cdots\)
1944.2.a.d	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.d	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{5}+3q^{7}-2q^{11}+q^{13}-4q^{17}+\cdots\)
1944.2.a.e	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.e	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{5}+2q^{11}-2q^{13}+4q^{17}-q^{19}+\cdots\)
1944.2.a.f	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.e	$1$	$1$	\(0\)	\(0\)	\(1\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{5}-2q^{11}-2q^{13}-4q^{17}-q^{19}+\cdots\)
1944.2.a.g	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.b	$1$	$1$	\(0\)	\(0\)	\(2\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}-3q^{7}+2q^{11}+q^{13}-8q^{17}+\cdots\)
1944.2.a.h	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.c	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+2q^{11}+q^{13}-2q^{17}+5q^{19}+\cdots\)
1944.2.a.i	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.d	$1$	$0$	\(0\)	\(0\)	\(2\)	\(3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{5}+3q^{7}+2q^{11}+q^{13}+4q^{17}+\cdots\)
1944.2.a.j	$1944$	$2$	1944.a	1.a	$1$	$1$	$1$	$15.523$	\(\Q\)	None	✓	✓			1944.2.a.a	$1$	$0$	\(0\)	\(0\)	\(4\)	\(3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{5}+3q^{7}-2q^{11}-5q^{13}+2q^{17}+\cdots\)
1944.2.a.k	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	\(\Q(\sqrt{3}) \)	None	✓	✓			1944.2.a.k	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{5}+2\beta q^{7}+(-1-3\beta )q^{11}+\cdots\)
1944.2.a.l	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	\(\Q(\sqrt{33}) \)	None	✓	✓			1944.2.a.l	$1$	$0$	\(0\)	\(0\)	\(-1\)	\(-3\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{5}+(-1-\beta )q^{7}+4q^{11}+(2-2\beta )q^{13}+\cdots\)
1944.2.a.m	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	\(\Q(\sqrt{33}) \)	None	✓	✓			1944.2.a.l	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{5}+(-1-\beta )q^{7}-4q^{11}+(2-2\beta )q^{13}+\cdots\)
1944.2.a.n	$1944$	$2$	1944.a	1.a	$1$	$2$	$2$	$15.523$	\(\Q(\sqrt{3}) \)	None	✓	✓			1944.2.a.k	$1$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{5}-2\beta q^{7}+(1-3\beta )q^{11}+\cdots\)
1944.2.a.o	$1944$	$2$	1944.a	1.a	$1$	$3$	$3$	$15.523$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		1944.2.a.o	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{5}+(-1+\beta _{1})q^{7}+(-1+2\beta _{1}+\cdots)q^{11}+\cdots\)
1944.2.a.p	$1944$	$2$	1944.a	1.a	$1$	$3$	$3$	$15.523$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓		1944.2.a.o	$1$	$1$	\(0\)	\(0\)	\(0\)	\(-3\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{5}+(-1+\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{11}+\cdots\)
1944.2.a.q	$1944$	$2$	1944.a	1.a	$1$	$6$	$6$	$15.523$	6.6.9926793.1	None	✓	✓	✓		1944.2.a.q	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$-$	$+$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(-\beta _{1}-\beta _{3}+\cdots)q^{11}+\cdots\)
1944.2.a.r	$1944$	$2$	1944.a	1.a	$1$	$6$	$6$	$15.523$	6.6.9926793.1	None	✓	✓	✓		1944.2.a.q	$1$	$0$	\(0\)	\(0\)	\(0\)	\(3\)		$+$	$-$	$-$	$3^{2}$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{5}+(1-\beta _{4})q^{7}+(\beta _{1}+\beta _{3}+\beta _{5})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1944))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1944)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(243))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(486))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(972))\)\(^{\oplus 2}\)