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

• Label: 154.2.e
• Level: $154$
• Weight: $2$
• Character orbit: 154.e
• Rep. character: $\chi_{154}(23,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $16$
• Newform subspaces: $6$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	56	16	40
Cusp forms	40	16	24
Eisenstein series	16	0	16

Trace form

16 * q - 8 * q^4 + 4 * q^5 + 8 * q^6 - 8 * q^7 - 16 * q^9 + 8 * q^13 - 8 * q^14 + 8 * q^15 - 8 * q^16 - 12 * q^17 + 8 * q^18 - 8 * q^20 + 16 * q^21 + 16 * q^23 - 4 * q^24 - 8 * q^25 + 12 * q^26 - 24 * q^27 + 4 * q^28 + 8 * q^29 - 8 * q^30 + 4 * q^31 + 4 * q^33 - 8 * q^34 + 4 * q^35 + 32 * q^36 + 8 * q^37 + 4 * q^38 + 4 * q^39 - 24 * q^41 - 20 * q^42 - 40 * q^43 - 4 * q^45 - 4 * q^46 - 16 * q^47 + 16 * q^49 - 32 * q^50 + 12 * q^51 - 4 * q^52 + 36 * q^53 - 16 * q^54 + 4 * q^56 - 56 * q^57 + 20 * q^58 + 4 * q^59 - 4 * q^60 - 36 * q^61 + 24 * q^62 - 20 * q^63 + 16 * q^64 + 4 * q^65 + 8 * q^66 - 4 * q^67 - 12 * q^68 + 24 * q^69 + 44 * q^70 - 8 * q^71 + 8 * q^72 + 16 * q^73 + 12 * q^74 + 60 * q^75 + 4 * q^77 - 16 * q^78 + 20 * q^79 + 4 * q^80 - 8 * q^81 + 8 * q^82 + 40 * q^83 + 4 * q^84 + 64 * q^85 + 4 * q^86 - 12 * q^87 + 72 * q^90 + 44 * q^91 - 32 * q^92 - 12 * q^93 + 8 * q^94 + 4 * q^95 - 4 * q^96 - 96 * q^97 - 48 * q^98

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.e.a	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	\(\Q(\sqrt{-3}) \)	None		✓			154.2.e.a	$2$	$1$	\(-1\)	\(-3\)	\(-2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.b	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	\(\Q(\sqrt{-3}) \)	None		✓			154.2.e.b	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.c	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	\(\Q(\sqrt{-3}) \)	None		✓			154.2.e.c	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.d	$154$	$2$	154.e	7.c	$3$	$2$	$1$	$1.230$	\(\Q(\sqrt{-3}) \)	None		✓			154.2.e.d	$2$	$0$	\(1\)	\(3\)	\(4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
154.2.e.e	$154$	$2$	154.e	7.c	$3$	$4$	$2$	$1.230$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓			154.2.e.e	$2$	$0$	\(-2\)	\(2\)	\(4\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
154.2.e.f	$154$	$2$	154.e	7.c	$3$	$4$	$2$	$1.230$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		✓			154.2.e.f	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}+\beta _{2}q^{4}+\cdots\)

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

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