Space of modular forms of level 163, weight 2, and trivial character

• Label: 163.2.a
• Level: $163$
• Weight: $2$
• Character orbit: 163.a
• Rep. character: $\chi_{163}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $3$
• Sturm bound: $27$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	163.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(27\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(163))\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	13	13	0
Eisenstein series	1	1	0

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

\(163\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(6\)	\(6\)	\(0\)		\(6\)	\(6\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(8\)	\(8\)	\(0\)		\(7\)	\(7\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

13 * q - 2 * q^2 - 4 * q^3 + 12 * q^4 - 2 * q^5 - 6 * q^6 - 4 * q^7 - 12 * q^8 + 7 * q^9 + 6 * q^10 - 2 * q^11 - 10 * q^12 + 2 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^18 - 4 * q^19 - 10 * q^20 - 18 * q^21 - 2 * q^22 + 10 * q^24 + 25 * q^25 + 2 * q^26 - 22 * q^27 - 16 * q^28 - 10 * q^29 + 30 * q^30 - 10 * q^31 - 26 * q^32 - 12 * q^33 + 24 * q^34 + 2 * q^35 + 18 * q^36 - 6 * q^37 + 6 * q^38 + 10 * q^39 + 24 * q^40 + 11 * q^41 + 40 * q^42 - 7 * q^43 + 12 * q^44 - 14 * q^45 - 36 * q^46 + 9 * q^47 - 16 * q^48 + q^49 + 14 * q^50 + 28 * q^51 - 14 * q^52 - 7 * q^53 - 24 * q^54 + 8 * q^55 + 20 * q^57 + 6 * q^58 + 6 * q^59 - 54 * q^60 - 3 * q^61 + 26 * q^62 + 16 * q^63 - 10 * q^64 + 44 * q^65 - 18 * q^66 - 22 * q^67 - 24 * q^68 + 4 * q^69 - 38 * q^70 + 23 * q^71 - 40 * q^72 - 14 * q^73 - 12 * q^74 + 10 * q^75 - 26 * q^76 - 10 * q^77 - 2 * q^78 - 22 * q^79 - 36 * q^80 + 13 * q^81 + 11 * q^83 - 64 * q^84 + 40 * q^85 + 48 * q^86 + 50 * q^87 - 22 * q^88 + 4 * q^89 + 14 * q^90 - 28 * q^91 + 42 * q^92 - 30 * q^93 + 56 * q^94 - 30 * q^95 + 84 * q^96 + 33 * q^97 - 14 * q^98 + 18 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(163))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		163
163.2.a.a	$163$	$2$	163.a	1.a	$1$	$1$	$1$	$1.302$	\(\Q\)	None	✓	✓			163.2.a.a	$1$	$1$	\(0\)	\(0\)	\(-4\)	\(2\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}-4q^{5}+2q^{7}-3q^{9}-6q^{11}+\cdots\)
163.2.a.b	$163$	$2$	163.a	1.a	$1$	$5$	$5$	$1.302$	5.5.65657.1	None	✓	✓	✓		163.2.a.b	$1$	$1$	\(-5\)	\(-5\)	\(-9\)	\(-6\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
163.2.a.c	$163$	$2$	163.a	1.a	$1$	$7$	$7$	$1.302$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	163.2.a.c	$1$	$0$	\(3\)	\(1\)	\(11\)	\(0\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(2-\beta _{6})q^{5}+\cdots\)