Space of modular forms of level 1472, weight 2, and trivial character

• Label: 1472.2.a
• Level: $1472$
• Weight: $2$
• Character orbit: 1472.a
• Rep. character: $\chi_{1472}(1,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $26$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1472))\).

	Total	New	Old
Modular forms	204	44	160
Cusp forms	181	44	137
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.

\(2\)	\(23\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(45\)	\(10\)	\(35\)		\(40\)	\(10\)	\(30\)		\(5\)	\(0\)	\(5\)
\(+\)	\(-\)	\(-\)		\(57\)	\(13\)	\(44\)		\(51\)	\(13\)	\(38\)		\(6\)	\(0\)	\(6\)
\(-\)	\(+\)	\(-\)		\(51\)	\(12\)	\(39\)		\(45\)	\(12\)	\(33\)		\(6\)	\(0\)	\(6\)
\(-\)	\(-\)	\(+\)		\(51\)	\(9\)	\(42\)		\(45\)	\(9\)	\(36\)		\(6\)	\(0\)	\(6\)
Plus space		\(+\)		\(96\)	\(19\)	\(77\)		\(85\)	\(19\)	\(66\)		\(11\)	\(0\)	\(11\)
Minus space		\(-\)		\(108\)	\(25\)	\(83\)		\(96\)	\(25\)	\(71\)		\(12\)	\(0\)	\(12\)

Trace form

\( 44 q + 44 q^{9} + 16 q^{13} - 8 q^{17} + 16 q^{21} + 36 q^{25} - 16 q^{33} + 16 q^{37} - 24 q^{41} + 44 q^{49} - 16 q^{57} + 16 q^{61} + 8 q^{73} + 28 q^{81} + 8 q^{89} - 8 q^{93} - 40 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1472))\) 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	23
1472.2.a.a	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.d	$1$	$0$	\(0\)	\(-3\)	\(0\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots\)
1472.2.a.b	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				92.2.a.a	$1$	$0$	\(0\)	\(-3\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}+2q^{5}+4q^{7}+6q^{9}+2q^{11}+\cdots\)
1472.2.a.c	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				92.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
1472.2.a.d	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.b	$1$	$1$	\(0\)	\(-1\)	\(2\)	\(4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+2q^{5}+4q^{7}-2q^{9}-2q^{11}+\cdots\)
1472.2.a.e	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(4\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
1472.2.a.f	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				46.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}-4q^{7}-3q^{9}-2q^{11}+2q^{13}+\cdots\)
1472.2.a.g	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				46.2.a.a	$1$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{5}+4q^{7}-3q^{9}+2q^{11}+2q^{13}+\cdots\)
1472.2.a.h	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
1472.2.a.i	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.c	$1$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots\)
1472.2.a.j	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				92.2.a.b	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{7}-2q^{9}+q^{13}-6q^{17}+\cdots\)
1472.2.a.k	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.b	$1$	$1$	\(0\)	\(1\)	\(2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}-4q^{7}-2q^{9}+2q^{11}+\cdots\)
1472.2.a.l	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.a	$1$	$0$	\(0\)	\(1\)	\(4\)	\(2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+4q^{5}+2q^{7}-2q^{9}+4q^{11}+\cdots\)
1472.2.a.m	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				184.2.a.d	$1$	$0$	\(0\)	\(3\)	\(0\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{7}+6q^{9}+5q^{13}-6q^{17}+\cdots\)
1472.2.a.n	$1472$	$2$	1472.a	1.a	$1$	$1$	$1$	$11.754$	\(\Q\)	None	✓				92.2.a.a	$1$	$0$	\(0\)	\(3\)	\(2\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+2q^{5}-4q^{7}+6q^{9}-2q^{11}+\cdots\)
1472.2.a.o	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{2}) \)	None	✓				736.2.a.a	$1$	$1$	\(0\)	\(-2\)	\(4\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
1472.2.a.p	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{17}) \)	None	✓				184.2.a.e	$1$	$1$	\(0\)	\(-1\)	\(-4\)	\(0\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{3}-2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)
1472.2.a.q	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{3}) \)	None	✓				736.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{5}+(-3+\beta )q^{7}+\cdots\)
1472.2.a.r	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{3}) \)	None	✓				736.2.a.b	$1$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1+\beta )q^{5}+(3+\beta )q^{7}+(-3+\cdots)q^{11}+\cdots\)
1472.2.a.s	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(-2\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1-\beta )q^{5}+(-1-\beta )q^{7}+2q^{9}+\cdots\)
1472.2.a.t	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{5}) \)	None	✓				23.2.a.a	$1$	$0$	\(0\)	\(0\)	\(2\)	\(2\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{3}+(1+\beta )q^{5}+(1-\beta )q^{7}+2q^{9}+\cdots\)
1472.2.a.u	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{17}) \)	None	✓				184.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)
1472.2.a.v	$1472$	$2$	1472.a	1.a	$1$	$2$	$2$	$11.754$	\(\Q(\sqrt{2}) \)	None	✓				736.2.a.a	$1$	$0$	\(0\)	\(2\)	\(4\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(2+\beta )q^{7}+\cdots\)
1472.2.a.w	$1472$	$2$	1472.a	1.a	$1$	$3$	$3$	$11.754$	3.3.316.1	None	✓		✓		736.2.a.e	$1$	$1$	\(0\)	\(-4\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1472.2.a.x	$1472$	$2$	1472.a	1.a	$1$	$3$	$3$	$11.754$	3.3.316.1	None	✓		✓		736.2.a.e	$1$	$0$	\(0\)	\(4\)	\(2\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{1})q^{3}+(1-\beta _{1}+\beta _{2})q^{5}+(1+\cdots)q^{7}+\cdots\)
1472.2.a.y	$1472$	$2$	1472.a	1.a	$1$	$4$	$4$	$11.754$	4.4.13768.1	None	✓		✓		736.2.a.g	$1$	$1$	\(0\)	\(-2\)	\(-6\)	\(-4\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
1472.2.a.z	$1472$	$2$	1472.a	1.a	$1$	$4$	$4$	$11.754$	4.4.13768.1	None	✓		✓		736.2.a.g	$1$	$0$	\(0\)	\(2\)	\(-6\)	\(4\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{3}+(-2+\beta _{3})q^{5}+(1-\beta _{1})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1472))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1472)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(736))\)\(^{\oplus 2}\)