Space of modular forms of level 153, weight 4, and trivial character

• Label: 153.4.a
• Level: $153$
• Weight: $4$
• Character orbit: 153.a
• Rep. character: $\chi_{153}(1,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $9$
• Sturm bound: $72$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(72\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(153))\).

	Total	New	Old
Modular forms	58	20	38
Cusp forms	50	20	30
Eisenstein series	8	0	8

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

\(3\)	\(17\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(4\)
\(+\)	\(-\)	\(-\)	\(4\)
\(-\)	\(+\)	\(-\)	\(5\)
\(-\)	\(-\)	\(+\)	\(7\)
Plus space		\(+\)	\(11\)
Minus space		\(-\)	\(9\)

Trace form

\( 20 q - 2 q^{2} + 90 q^{4} + 2 q^{5} - 46 q^{7} - 30 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(153))\) 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	17
153.4.a.a	$153$	$4$	153.a	1.a	$1$	$1$	$1$	$9.027$	\(\Q\)	None	✓				51.4.a.c	$1$	$1$	\(-1\)	\(0\)	\(10\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-7q^{4}+10q^{5}-8q^{7}+15q^{8}+\cdots\)
153.4.a.b	$153$	$4$	153.a	1.a	$1$	$1$	$1$	$9.027$	\(\Q\)	None	✓				51.4.a.a	$1$	$0$	\(1\)	\(0\)	\(-16\)	\(34\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-7q^{4}-2^{4}q^{5}+34q^{7}-15q^{8}+\cdots\)
153.4.a.c	$153$	$4$	153.a	1.a	$1$	$1$	$1$	$9.027$	\(\Q\)	None	✓				51.4.a.b	$1$	$0$	\(1\)	\(0\)	\(20\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-7q^{4}+20q^{5}-2q^{7}-15q^{8}+\cdots\)
153.4.a.d	$153$	$4$	153.a	1.a	$1$	$1$	$1$	$9.027$	\(\Q\)	None	✓				17.4.a.a	$1$	$1$	\(3\)	\(0\)	\(-6\)	\(-28\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3q^{2}+q^{4}-6q^{5}-28q^{7}-21q^{8}+\cdots\)
153.4.a.e	$153$	$4$	153.a	1.a	$1$	$2$	$2$	$9.027$	\(\Q(\sqrt{2}) \)	None	✓				51.4.a.d	$1$	$0$	\(0\)	\(0\)	\(-6\)	\(-8\)		$-$	$-$	$+$	$3$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+10q^{4}+(-3+4\beta )q^{5}+(-4+\cdots)q^{7}+\cdots\)
153.4.a.f	$153$	$4$	153.a	1.a	$1$	$3$	$3$	$9.027$	3.3.5912.1	None	✓		✓		51.4.a.e	$1$	$1$	\(-5\)	\(0\)	\(-8\)	\(-8\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-2+\beta _{1})q^{2}+(5-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
153.4.a.g	$153$	$4$	153.a	1.a	$1$	$3$	$3$	$9.027$	3.3.2636.1	None	✓		✓		17.4.a.b	$1$	$0$	\(-1\)	\(0\)	\(8\)	\(22\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(8-3\beta _{1}-\beta _{2})q^{4}+\cdots\)
153.4.a.h	$153$	$4$	153.a	1.a	$1$	$4$	$4$	$9.027$	4.4.1506848.1	None	✓	✓	✓	✓	153.4.a.h	$1$	$1$	\(-4\)	\(0\)	\(-22\)	\(-24\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{2}+(6+2\beta _{2}-\beta _{3})q^{4}+\cdots\)
153.4.a.i	$153$	$4$	153.a	1.a	$1$	$4$	$4$	$9.027$	4.4.1506848.1	None	✓	✓	✓	✓	153.4.a.h	$1$	$0$	\(4\)	\(0\)	\(22\)	\(-24\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{2})q^{2}+(6-2\beta _{2}-\beta _{3})q^{4}+(5+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(153))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(153)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 2}\)