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

• Label: 154.2.m
• Level: $154$
• Weight: $2$
• Character orbit: 154.m
• Rep. character: $\chi_{154}(9,\cdot)$
• Character field: $\Q(\zeta_{15})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.m (of order \(15\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q(\zeta_{15})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	224	64	160
Cusp forms	160	64	96
Eisenstein series	64	0	64

Trace form

64 * q + 8 * q^4 - 4 * q^5 - 8 * q^6 - 2 * q^7 - 4 * q^9 - 20 * q^10 - 8 * q^13 - 2 * q^14 + 12 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 + 8 * q^20 - 16 * q^21 - 16 * q^23 + 4 * q^24 - 12 * q^25 + 8 * q^26 - 36 * q^27 - 14 * q^28 - 28 * q^29 + 8 * q^30 + 6 * q^31 + 46 * q^33 - 32 * q^34 - 34 * q^35 - 32 * q^36 - 8 * q^37 - 4 * q^38 - 24 * q^39 + 10 * q^40 - 56 * q^41 - 10 * q^42 + 40 * q^43 + 10 * q^44 + 4 * q^45 + 4 * q^46 - 44 * q^47 - 46 * q^49 + 32 * q^50 + 8 * q^51 + 4 * q^52 - 16 * q^53 - 64 * q^54 - 20 * q^55 - 4 * q^56 - 24 * q^57 + 20 * q^58 - 4 * q^59 + 4 * q^60 - 34 * q^61 + 16 * q^62 - 10 * q^63 - 16 * q^64 + 56 * q^65 + 32 * q^66 + 64 * q^67 + 2 * q^68 + 176 * q^69 + 6 * q^70 + 8 * q^71 + 12 * q^72 - 6 * q^73 + 8 * q^74 + 20 * q^75 + 40 * q^76 + 6 * q^77 + 96 * q^78 + 10 * q^79 + 6 * q^80 + 88 * q^81 + 12 * q^82 + 80 * q^83 + 36 * q^84 - 44 * q^85 + 26 * q^86 + 112 * q^87 + 10 * q^88 + 20 * q^89 + 88 * q^90 + 6 * q^91 - 28 * q^92 + 22 * q^93 + 52 * q^94 - 74 * q^95 + 4 * q^96 + 36 * q^97 + 48 * q^98 - 160 * 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.m.a	$154$	$2$	154.m	77.m	$15$	$8$	$1$	$1.230$	\(\Q(\zeta_{15})\)	None		✓			154.2.m.a	$4$	$0$	\(-1\)	\(1\)	\(-5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q-\zeta_{15}^{7}q^{2}+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
154.2.m.b	$154$	$2$	154.m	77.m	$15$	$24$	$3$	$1.230$		None		✓			154.2.m.b	$4$	$0$	\(-3\)	\(-3\)	\(3\)	\(-5\)		$\mathrm{SU}(2)[C_{15}]$
154.2.m.c	$154$	$2$	154.m	77.m	$15$	$32$	$4$	$1.230$		None		✓	✓		154.2.m.c	$4$	$0$	\(4\)	\(2\)	\(-2\)	\(7\)		$\mathrm{SU}(2)[C_{15}]$

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

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