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

• Label: 153.2.l
• Level: $153$
• Weight: $2$
• Character orbit: 153.l
• Rep. character: $\chi_{153}(19,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $28$
• Newform subspaces: $5$
• Sturm bound: $36$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.l (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(36\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

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

	Total	New	Old
Modular forms	88	36	52
Cusp forms	56	28	28
Eisenstein series	32	8	24

Trace form

28 * q + 4 * q^2 + 8 * q^5 - 4 * q^7 - 4 * q^8 - 4 * q^10 - 4 * q^11 + 12 * q^14 - 36 * q^16 + 8 * q^17 - 24 * q^19 - 20 * q^20 - 36 * q^22 - 12 * q^23 + 4 * q^25 - 12 * q^26 + 52 * q^28 + 4 * q^29 + 4 * q^31 - 4 * q^32 - 36 * q^34 - 40 * q^35 + 88 * q^40 + 28 * q^41 - 24 * q^43 + 20 * q^44 + 20 * q^46 + 24 * q^49 + 12 * q^50 + 80 * q^52 + 36 * q^53 + 36 * q^56 - 64 * q^58 - 16 * q^59 - 48 * q^61 - 4 * q^62 - 20 * q^65 - 48 * q^67 - 12 * q^68 - 104 * q^70 - 4 * q^71 - 52 * q^73 - 84 * q^74 + 8 * q^76 - 8 * q^77 - 4 * q^79 + 16 * q^80 - 84 * q^82 - 48 * q^83 + 60 * q^85 + 24 * q^86 + 172 * q^88 + 32 * q^91 + 60 * q^92 + 88 * q^94 + 48 * q^95 + 40 * q^97

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.l.a	$153$	$2$	153.l	17.d	$8$	$4$	$1$	$1.222$	\(\Q(\zeta_{8})\)	None		✓			153.2.l.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q-\zeta_{8}^{3}q^{2}+\zeta_{8}^{2}q^{4}+(-1+\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
153.2.l.b	$153$	$2$	153.l	17.d	$8$	$4$	$1$	$1.222$	\(\Q(\zeta_{8})\)	None		✓			153.2.l.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{8}^{3}q^{2}+\zeta_{8}^{2}q^{4}+(1-\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
153.2.l.c	$153$	$2$	153.l	17.d	$8$	$4$	$1$	$1.222$	\(\Q(\zeta_{8})\)	None					17.2.d.a	$2$	$0$	\(4\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{2}+(2\zeta_{8}-\zeta_{8}^{2}+\cdots)q^{4}+\cdots\)
153.2.l.d	$153$	$2$	153.l	17.d	$8$	$8$	$2$	$1.222$	8.0.\(\cdots\).13	None		✓			153.2.l.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(-\beta _{5}+\beta _{7})q^{2}+(-\beta _{2}+4\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
153.2.l.e	$153$	$2$	153.l	17.d	$8$	$8$	$2$	$1.222$	\(\Q(\zeta_{16})\)	None					51.2.h.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+(\zeta_{16}+\zeta_{16}^{3})q^{2}+(\zeta_{16}^{2}+\zeta_{16}^{6}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(153, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)