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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(17\)	\(4\)	\(13\)		\(15\)	\(4\)	\(11\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(13\)	\(4\)	\(9\)		\(11\)	\(4\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(14\)	\(5\)	\(9\)		\(12\)	\(5\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(14\)	\(7\)	\(7\)		\(12\)	\(7\)	\(5\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(31\)	\(11\)	\(20\)		\(27\)	\(11\)	\(16\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(27\)	\(9\)	\(18\)		\(23\)	\(9\)	\(14\)		\(4\)	\(0\)	\(4\)

Trace form

20 * q - 2 * q^2 + 90 * q^4 + 2 * q^5 - 46 * q^7 - 30 * q^8 + 22 * q^10 + 36 * q^11 + 76 * q^13 + 112 * q^14 + 298 * q^16 + 34 * q^17 + 60 * q^19 + 130 * q^20 - 434 * q^22 - 82 * q^23 + 496 * q^25 + 4 * q^26 - 168 * q^28 - 6 * q^29 - 702 * q^31 + 338 * q^32 - 68 * q^34 + 20 * q^35 - 318 * q^37 + 380 * q^38 + 542 * q^40 - 804 * q^41 + 848 * q^43 + 90 * q^44 - 284 * q^46 - 1032 * q^47 + 220 * q^49 - 862 * q^50 - 1784 * q^52 + 12 * q^53 - 908 * q^55 + 960 * q^56 + 1654 * q^58 - 816 * q^59 - 1982 * q^61 - 776 * q^62 + 3730 * q^64 + 596 * q^65 + 460 * q^67 + 408 * q^68 - 736 * q^70 + 3238 * q^71 - 2272 * q^73 - 914 * q^74 + 3344 * q^76 + 1104 * q^77 + 1666 * q^79 + 2434 * q^80 - 1568 * q^82 - 872 * q^83 - 578 * q^85 + 40 * q^86 - 6586 * q^88 + 1064 * q^89 + 1440 * q^91 - 4484 * q^92 - 696 * q^94 + 2800 * q^95 + 2356 * q^97 - 6042 * q^98

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

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