Space of modular forms of level 4923, weight 2, and trivial character

• Label: 4923.2.a
• Level: $4923$
• Weight: $2$
• Character orbit: 4923.a
• Rep. character: $\chi_{4923}(1,\cdot)$
• Character field: $\Q$
• Dimension: $228$
• Newform subspaces: $17$
• Sturm bound: $1096$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 4923 = 3^{2} \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4923.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1096\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4923))\).

	Total	New	Old
Modular forms	552	228	324
Cusp forms	545	228	317
Eisenstein series	7	0	7

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

\(3\)	\(547\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(40\)
\(+\)	\(-\)	$-$	\(52\)
\(-\)	\(+\)	$-$	\(71\)
\(-\)	\(-\)	$+$	\(65\)
Plus space		\(+\)	\(105\)
Minus space		\(-\)	\(123\)

Trace form

\( 228 q + q^{2} + 225 q^{4} + 4 q^{5} - 2 q^{7} + 3 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4923))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	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	547
4923.2.a.a	$4923$	$2$	4923.a	1.a	$1$	$1$	$1$	$39.310$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-2q^{7}+3q^{11}+5q^{13}+4q^{16}+\cdots\)
4923.2.a.b	$4923$	$2$	4923.a	1.a	$1$	$1$	$1$	$39.310$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}-2q^{7}+4q^{10}+\cdots\)
4923.2.a.c	$4923$	$2$	4923.a	1.a	$1$	$1$	$1$	$39.310$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}-2q^{7}+4q^{10}+\cdots\)
4923.2.a.d	$4923$	$2$	4923.a	1.a	$1$	$1$	$1$	$39.310$	\(\Q\)	None	✓	$1$	$1$	\(2\)	\(0\)	\(2\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+2q^{5}-2q^{7}+4q^{10}+\cdots\)
4923.2.a.e	$4923$	$2$	4923.a	1.a	$1$	$2$	$2$	$39.310$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{4}+(-2+3\beta )q^{5}+\cdots\)
4923.2.a.f	$4923$	$2$	4923.a	1.a	$1$	$2$	$2$	$39.310$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{5}-3\beta q^{7}-2\beta q^{8}-2q^{10}+\cdots\)
4923.2.a.g	$4923$	$2$	4923.a	1.a	$1$	$2$	$2$	$39.310$	\(\Q(\sqrt{3}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{4}+2\beta q^{5}+2q^{7}-\beta q^{8}+\cdots\)
4923.2.a.h	$4923$	$2$	4923.a	1.a	$1$	$2$	$2$	$39.310$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+\beta q^{5}+2q^{7}+\cdots\)
4923.2.a.i	$4923$	$2$	4923.a	1.a	$1$	$3$	$3$	$39.310$	\(\Q(\zeta_{14})^+\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{2}q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)
4923.2.a.j	$4923$	$2$	4923.a	1.a	$1$	$8$	$8$	$39.310$	8.8.4230320128.1	None	✓	$1$	$1$	\(2\)	\(0\)	\(4\)	\(-8\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4923.2.a.k	$4923$	$2$	4923.a	1.a	$1$	$17$	$17$	$39.310$	\(\mathbb{Q}[x]/(x^{17} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(6\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{12}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
4923.2.a.l	$4923$	$2$	4923.a	1.a	$1$	$18$	$18$	$39.310$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(4\)	\(0\)	\(27\)	\(-11\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+\beta _{3})q^{5}+\cdots\)
4923.2.a.m	$4923$	$2$	4923.a	1.a	$1$	$24$	$24$	$39.310$		None	✓	$1$	$1$	\(-8\)	\(0\)	\(-8\)	\(1\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4923.2.a.n	$4923$	$2$	4923.a	1.a	$1$	$25$	$25$	$39.310$		None	✓	$1$	$1$	\(-4\)	\(0\)	\(-29\)	\(5\)		$-$	$-$	$+$		$\mathrm{SU}(2)$
4923.2.a.o	$4923$	$2$	4923.a	1.a	$1$	$31$	$31$	$39.310$		None	✓	$1$	$0$	\(-3\)	\(0\)	\(0\)	\(17\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
4923.2.a.p	$4923$	$2$	4923.a	1.a	$1$	$40$	$40$	$39.310$		None	✓	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-20\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
4923.2.a.q	$4923$	$2$	4923.a	1.a	$1$	$50$	$50$	$39.310$		None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4923))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4923)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1641))\)\(^{\oplus 2}\)