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

\( 64 q + 8 q^{4} - 4 q^{5} - 8 q^{6} - 2 q^{7} - 4 q^{9} + O(q^{10}) \)

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	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		$4$	$0$	\(-1\)	\(1\)	\(-5\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{15}]$	\(q-\zeta_{15}^{7}q^{2}+(2\zeta_{15}-\zeta_{15}^{2}-\zeta_{15}^{5}+\cdots)q^{3}+\cdots\)
154.2.m.b	$154$	$2$	154.m	77.m	$15$	$24$	$3$	$1.230$		None		$4$	$0$	\(-3\)	\(-3\)	\(3\)	\(-5\)		$\mathrm{SU}(2)[C_{15}]$
154.2.m.c	$154$	$2$	154.m	77.m	$15$	$32$	$4$	$1.230$		None		$4$	$0$	\(4\)	\(2\)	\(-2\)	\(7\)		$\mathrm{SU}(2)[C_{15}]$

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

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