Space of modular forms of level 154, weight 2, and trivial character

• Label: 154.2.a
• Level: $154$
• Weight: $2$
• Character orbit: 154.a
• Rep. character: $\chi_{154}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 154 = 2 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	154.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(154))\).

	Total	New	Old
Modular forms	28	5	23
Cusp forms	21	5	16
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(7\)	\(11\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(2\)	\(1\)	\(1\)		\(2\)	\(1\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(4\)	\(1\)	\(3\)		\(3\)	\(1\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(5\)	\(0\)	\(5\)		\(4\)	\(0\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(3\)	\(1\)	\(2\)		\(2\)	\(1\)	\(1\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(4\)	\(0\)	\(4\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(4\)	\(2\)	\(2\)		\(3\)	\(2\)	\(1\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(12\)	\(1\)	\(11\)		\(9\)	\(1\)	\(8\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(16\)	\(4\)	\(12\)		\(12\)	\(4\)	\(8\)		\(4\)	\(0\)	\(4\)

Trace form

5 * q + q^2 + 5 * q^4 + 2 * q^5 - 4 * q^6 - q^7 + q^8 + q^9 + 6 * q^10 + q^11 - 2 * q^13 + 3 * q^14 - 8 * q^15 + 5 * q^16 - 6 * q^17 + 5 * q^18 - 12 * q^19 + 2 * q^20 - 4 * q^21 + q^22 + 8 * q^23 - 4 * q^24 + 11 * q^25 + 2 * q^26 - 24 * q^27 - q^28 - 2 * q^29 - 16 * q^30 - 16 * q^31 + q^32 + 2 * q^34 + 2 * q^35 + q^36 - 2 * q^37 - 8 * q^38 - 16 * q^39 + 6 * q^40 + 18 * q^41 - 20 * q^43 + q^44 + 34 * q^45 - 8 * q^46 + 16 * q^47 + 5 * q^49 - 9 * q^50 + 24 * q^51 - 2 * q^52 + 6 * q^53 - 16 * q^54 + 6 * q^55 + 3 * q^56 + 8 * q^57 - 2 * q^58 + 8 * q^59 - 8 * q^60 - 18 * q^61 + 8 * q^62 + 11 * q^63 + 5 * q^64 - 4 * q^65 - 4 * q^66 - 20 * q^67 - 6 * q^68 - 2 * q^70 + 8 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 - 24 * q^75 - 12 * q^76 + 3 * q^77 + 16 * q^79 + 2 * q^80 + 29 * q^81 + 10 * q^82 - 4 * q^83 - 4 * q^84 - 4 * q^85 + 4 * q^86 + 24 * q^87 + q^88 + 18 * q^89 + 6 * q^90 - 2 * q^91 + 8 * q^92 - 24 * q^93 - 8 * q^94 + 32 * q^95 - 4 * q^96 + 18 * q^97 + q^98 + 13 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(154))\) 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					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	7	11
154.2.a.a	$154$	$2$	154.a	1.a	$1$	$1$	$1$	$1.230$	\(\Q\)	None	✓	✓	✓	✓	154.2.a.a	$1$	$1$	\(-1\)	\(0\)	\(-4\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{4}-4q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
154.2.a.b	$154$	$2$	154.a	1.a	$1$	$1$	$1$	$1.230$	\(\Q\)	None	✓	✓	✓	✓	154.2.a.b	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(-1\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{7}+\cdots\)
154.2.a.c	$154$	$2$	154.a	1.a	$1$	$1$	$1$	$1.230$	\(\Q\)	None	✓	✓	✓	✓	154.2.a.c	$1$	$0$	\(1\)	\(0\)	\(2\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{4}+2q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
154.2.a.d	$154$	$2$	154.a	1.a	$1$	$2$	$2$	$1.230$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	154.2.a.d	$1$	$0$	\(2\)	\(-2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(1+\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(154))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(154)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 2}\)