Space of modular forms of level 153, weight 2, and Character 153.d

• Label: 153.2.d
• Level: $153$
• Weight: $2$
• Character orbit: 153.d
• Rep. character: $\chi_{153}(118,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $36$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(36\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(153, [\chi])\).

	Total	New	Old
Modular forms	22	8	14
Cusp forms	14	6	8
Eisenstein series	8	2	6

Trace form

\( 6 q + 2 q^{2} - 2 q^{4} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(153, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
153.2.d.a	$153$	$2$	153.d	17.b	$2$	$2$	$2$	$1.222$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-q^{4}+iq^{7}+3q^{8}+iq^{11}+\cdots\)
153.2.d.b	$153$	$2$	153.d	17.b	$2$	$2$	$2$	$1.222$	\(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{-51}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{4}+\beta q^{5}+\beta q^{11}-q^{13}+4q^{16}+\cdots\)
153.2.d.c	$153$	$2$	153.d	17.b	$2$	$2$	$2$	$1.222$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{2}+2q^{4}+3iq^{5}-2iq^{7}+6iq^{10}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(153, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(153, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)