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

• Label: 153.2.f
• Level: $153$
• Weight: $2$
• Character orbit: 153.f
• Rep. character: $\chi_{153}(55,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	44	16	28
Cusp forms	28	12	16
Eisenstein series	16	4	12

Trace form

12 * q - 12 * q^4 + 4 * q^5 - 4 * q^10 - 8 * q^13 - 24 * q^14 - 4 * q^16 + 4 * q^17 + 12 * q^20 + 8 * q^22 + 16 * q^23 - 8 * q^28 - 4 * q^29 + 8 * q^31 + 8 * q^34 - 8 * q^35 + 12 * q^37 - 24 * q^38 + 28 * q^40 - 28 * q^41 + 32 * q^44 + 8 * q^47 + 60 * q^50 - 16 * q^52 - 8 * q^55 + 24 * q^56 + 28 * q^58 - 4 * q^61 - 16 * q^62 - 28 * q^64 - 16 * q^65 - 32 * q^67 - 60 * q^68 - 24 * q^71 - 12 * q^73 + 28 * q^74 - 60 * q^80 + 4 * q^82 - 28 * q^85 + 8 * q^86 - 16 * q^88 + 8 * q^89 - 40 * q^91 - 56 * q^92 - 8 * q^95 + 28 * q^97 + 76 * q^98

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
153.2.f.a	$153$	$2$	153.f	17.c	$4$	$4$	$2$	$1.222$	\(\Q(\zeta_{8})\)	None		✓			153.2.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+\zeta_{8}q^{5}+(1-\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
153.2.f.b	$153$	$2$	153.f	17.c	$4$	$8$	$4$	$1.222$	8.0.836829184.2	None			✓		51.2.e.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(-2-\beta _{4}+\beta _{6})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)

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

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