Space of modular forms of level 154, weight 2, and Character 154.f

• Label: 154.2.f
• Level: $154$
• Weight: $2$
• Character orbit: 154.f
• Rep. character: $\chi_{154}(15,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $24$
• Newform subspaces: $5$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.f (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(154, [\chi])\).

	Total	New	Old
Modular forms	112	24	88
Cusp forms	80	24	56
Eisenstein series	32	0	32

Trace form

24 * q + 2 * q^2 + 8 * q^3 - 6 * q^4 + 4 * q^5 - 6 * q^6 + 2 * q^8 - 10 * q^9 - 10 * q^11 - 12 * q^12 + 4 * q^13 + 12 * q^15 - 6 * q^16 + 12 * q^17 - 2 * q^19 + 4 * q^20 - 8 * q^21 + 10 * q^22 - 24 * q^23 - 6 * q^24 - 30 * q^25 + 4 * q^26 + 26 * q^27 - 16 * q^29 - 20 * q^30 + 16 * q^31 - 8 * q^32 + 34 * q^33 + 28 * q^34 + 4 * q^35 - 4 * q^37 - 28 * q^38 - 24 * q^39 + 12 * q^41 - 52 * q^43 - 56 * q^45 - 8 * q^46 + 36 * q^47 + 8 * q^48 - 6 * q^49 - 10 * q^50 + 42 * q^51 - 16 * q^52 - 24 * q^53 + 64 * q^54 - 60 * q^55 - 10 * q^57 + 20 * q^58 - 66 * q^59 - 8 * q^60 + 24 * q^61 - 24 * q^62 - 6 * q^64 + 8 * q^65 + 8 * q^66 + 36 * q^67 + 12 * q^68 - 24 * q^69 + 8 * q^70 + 24 * q^71 + 10 * q^72 + 28 * q^73 + 52 * q^74 + 58 * q^75 + 28 * q^76 + 8 * q^77 + 32 * q^78 + 8 * q^79 + 4 * q^80 + 64 * q^81 + 14 * q^82 + 30 * q^83 - 8 * q^84 + 52 * q^85 - 14 * q^86 + 72 * q^87 + 10 * q^88 - 36 * q^89 - 28 * q^90 - 36 * q^91 + 16 * q^92 - 44 * q^93 + 32 * q^94 - 32 * q^95 + 4 * q^96 - 30 * q^97 - 8 * q^98 + 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(154, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
154.2.f.a	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	\(\Q(\zeta_{10})\)	None		✓			154.2.f.a	$2$	$0$	\(-1\)	\(1\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
154.2.f.b	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	\(\Q(\zeta_{10})\)	None		✓			154.2.f.b	$2$	$0$	\(-1\)	\(5\)	\(3\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
154.2.f.c	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	\(\Q(\zeta_{10})\)	None		✓			154.2.f.c	$2$	$0$	\(1\)	\(-2\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
154.2.f.d	$154$	$2$	154.f	11.c	$5$	$4$	$1$	$1.230$	\(\Q(\zeta_{10})\)	None		✓			154.2.f.d	$2$	$0$	\(1\)	\(5\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2\zeta_{10}+\cdots)q^{3}+\cdots\)
154.2.f.e	$154$	$2$	154.f	11.c	$5$	$8$	$2$	$1.230$	8.0.58140625.2	None		✓	✓		154.2.f.e	$2$	$0$	\(2\)	\(-1\)	\(5\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(1-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+(1-2\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(154, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(154, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)