Space of modular forms of level 153, weight 2, and trivial character

• Label: 153.2.a
• Level: $153$
• Weight: $2$
• Character orbit: 153.a
• Rep. character: $\chi_{153}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $5$
• Sturm bound: $36$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(36\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(153))\).

	Total	New	Old
Modular forms	22	6	16
Cusp forms	15	6	9
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.

\(3\)	\(17\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(7\)	\(1\)	\(6\)		\(5\)	\(1\)	\(4\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(6\)	\(3\)	\(3\)		\(4\)	\(3\)	\(1\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(6\)	\(1\)	\(5\)		\(4\)	\(1\)	\(3\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(9\)	\(2\)	\(7\)		\(6\)	\(2\)	\(4\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(13\)	\(4\)	\(9\)		\(9\)	\(4\)	\(5\)		\(4\)	\(0\)	\(4\)

Trace form

6 * q + 2 * q^2 + 6 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 4 * q^10 + 4 * q^11 - 8 * q^13 + 4 * q^14 - 2 * q^16 - 2 * q^17 - 4 * q^19 - 12 * q^20 + 4 * q^22 - 4 * q^23 - 2 * q^25 - 8 * q^26 - 4 * q^28 - 12 * q^29 + 12 * q^31 + 14 * q^32 + 2 * q^34 + 20 * q^35 + 12 * q^37 - 28 * q^38 - 28 * q^40 + 12 * q^41 - 4 * q^43 - 12 * q^44 + 20 * q^46 + 20 * q^47 - 2 * q^49 + 26 * q^50 - 12 * q^52 - 8 * q^53 + 4 * q^55 - 12 * q^56 + 4 * q^58 + 12 * q^61 + 20 * q^62 - 10 * q^64 + 16 * q^67 - 6 * q^68 - 12 * q^71 - 12 * q^73 - 20 * q^74 - 16 * q^76 - 12 * q^77 - 4 * q^79 - 44 * q^80 - 20 * q^82 + 20 * q^83 + 28 * q^86 - 4 * q^88 - 16 * q^89 + 16 * q^91 + 36 * q^92 + 72 * q^94 + 16 * q^95 - 12 * q^97 + 2 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(153))\) 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
153.2.a.a	$153$	$2$	153.a	1.a	$1$	$1$	$1$	$1.222$	\(\Q\)	None	✓	✓	✓	✓	153.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(-1\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-q^{5}-2q^{7}+2q^{10}+\cdots\)
153.2.a.b	$153$	$2$	153.a	1.a	$1$	$1$	$1$	$1.222$	\(\Q\)	None	✓		✓	✓	51.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-3q^{5}-4q^{7}+3q^{11}-q^{13}+\cdots\)
153.2.a.c	$153$	$2$	153.a	1.a	$1$	$1$	$1$	$1.222$	\(\Q\)	None	✓				17.2.a.a	$1$	$0$	\(1\)	\(0\)	\(2\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}+4q^{7}-3q^{8}+2q^{10}+\cdots\)
153.2.a.d	$153$	$2$	153.a	1.a	$1$	$1$	$1$	$1.222$	\(\Q\)	None	✓	✓	✓	✓	153.2.a.a	$1$	$0$	\(2\)	\(0\)	\(1\)	\(-2\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+q^{5}-2q^{7}+2q^{10}+\cdots\)
153.2.a.e	$153$	$2$	153.a	1.a	$1$	$2$	$2$	$1.222$	\(\Q(\sqrt{17}) \)	None	✓		✓		51.2.a.b	$1$	$0$	\(1\)	\(0\)	\(-3\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(2+\beta )q^{4}+(-1-\beta )q^{5}+(4+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(153))\) into lower level spaces

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