Space of modular forms of level 161, weight 2, and trivial character

• Label: 161.2.a
• Level: $161$
• Weight: $2$
• Character orbit: 161.a
• Rep. character: $\chi_{161}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $4$
• Sturm bound: $32$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(32\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(161))\).

	Total	New	Old
Modular forms	18	11	7
Cusp forms	15	11	4
Eisenstein series	3	0	3

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

\(7\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(6\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(9\)

Trace form

11 * q - q^2 + 15 * q^4 - 2 * q^5 + 2 * q^6 + q^7 - 3 * q^8 + 3 * q^9 - 10 * q^10 + 4 * q^11 - 6 * q^12 - 2 * q^13 + 3 * q^14 + 20 * q^15 + 19 * q^16 - 10 * q^17 - 15 * q^18 + 8 * q^19 - 6 * q^20 + 8 * q^22 - 5 * q^23 - 24 * q^24 + 13 * q^25 - 8 * q^26 + 12 * q^27 + 7 * q^28 - 2 * q^29 - 48 * q^30 + 24 * q^31 - 17 * q^32 - 24 * q^33 + 2 * q^34 - 2 * q^35 - 15 * q^36 - 2 * q^37 - 44 * q^38 + 8 * q^39 - 22 * q^40 - 14 * q^41 - 8 * q^42 - 12 * q^43 - 24 * q^44 - 6 * q^45 - q^46 + 16 * q^47 + 18 * q^48 + 11 * q^49 + 9 * q^50 - 8 * q^51 + 30 * q^53 + 6 * q^54 + 4 * q^55 + 15 * q^56 + 4 * q^57 + 4 * q^58 + 20 * q^60 - 6 * q^61 - 6 * q^62 + 13 * q^63 + 49 * q^64 - 32 * q^65 + 4 * q^66 + 24 * q^67 + 34 * q^68 + 4 * q^69 - 10 * q^70 - 31 * q^72 - 22 * q^73 + 38 * q^74 - 28 * q^75 + 64 * q^76 - 4 * q^77 + 50 * q^78 + 44 * q^79 - 34 * q^80 + 3 * q^81 - 20 * q^82 + 28 * q^83 + 12 * q^84 - 20 * q^85 + 44 * q^86 - 28 * q^87 - 36 * q^88 - 10 * q^89 + 38 * q^90 + 2 * q^91 - 5 * q^92 + 4 * q^93 - 22 * q^94 + 24 * q^95 + 2 * q^96 - 22 * q^97 - q^98 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(161))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		7	23
161.2.a.a	$161$	$2$	161.a	1.a	$1$	$1$	$1$	$1.286$	\(\Q\)	None	✓	✓			161.2.a.a	$1$	$0$	\(-1\)	\(0\)	\(2\)	\(1\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+2q^{5}+q^{7}+3q^{8}-3q^{9}+\cdots\)
161.2.a.b	$161$	$2$	161.a	1.a	$1$	$2$	$2$	$1.286$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	161.2.a.b	$1$	$1$	\(-1\)	\(-2\)	\(-2\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+(-2+2\beta )q^{5}+\cdots\)
161.2.a.c	$161$	$2$	161.a	1.a	$1$	$3$	$3$	$1.286$	3.3.148.1	None	✓	✓	✓	✓	161.2.a.c	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
161.2.a.d	$161$	$2$	161.a	1.a	$1$	$5$	$5$	$1.286$	5.5.2147108.1	None	✓	✓	✓		161.2.a.d	$1$	$0$	\(2\)	\(0\)	\(-4\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(161))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(161)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)