Space of modular forms of level 131, weight 2, and trivial character

• Label: 131.2.a
• Level: $131$
• Weight: $2$
• Character orbit: 131.a
• Rep. character: $\chi_{131}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	131.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(131))\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	11	11	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.

\(131\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(11\)	\(11\)	\(0\)		\(10\)	\(10\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

11 * q + 14 * q^4 + 2 * q^5 - 4 * q^6 - 6 * q^8 + 13 * q^9 + 2 * q^11 - 6 * q^12 + 8 * q^13 - 6 * q^14 + 32 * q^16 + 2 * q^17 - 24 * q^18 - 2 * q^19 - 10 * q^20 + 10 * q^21 - 4 * q^22 - 12 * q^23 - 36 * q^24 + 17 * q^25 - 28 * q^26 - 6 * q^27 - 22 * q^28 + 16 * q^29 - 52 * q^30 + 4 * q^31 - 42 * q^32 - 27 * q^33 - 4 * q^34 - 17 * q^35 + 20 * q^36 + 26 * q^37 - 8 * q^38 + 7 * q^39 + 10 * q^40 - 16 * q^41 + 2 * q^42 + 12 * q^43 + 18 * q^44 + 25 * q^45 + 32 * q^46 + 4 * q^47 + 10 * q^48 + 17 * q^49 + 8 * q^50 - 22 * q^51 + 10 * q^52 + 21 * q^53 + 12 * q^54 - 20 * q^55 - 6 * q^56 - 2 * q^57 - 4 * q^59 + 40 * q^60 + 36 * q^61 + 4 * q^62 - 15 * q^63 + 44 * q^64 - 8 * q^65 + 32 * q^66 - 16 * q^67 + 24 * q^68 + 20 * q^69 - 30 * q^70 + 10 * q^71 - 44 * q^72 - 10 * q^73 + 52 * q^74 - 15 * q^75 - 16 * q^76 - 24 * q^77 + 78 * q^78 + 16 * q^79 + 6 * q^80 + 19 * q^81 - 20 * q^82 - 18 * q^83 + 44 * q^84 + 8 * q^85 - 20 * q^86 - 48 * q^87 + 60 * q^88 + 3 * q^89 + 6 * q^90 + 2 * q^91 - 44 * q^92 + 2 * q^93 + 16 * q^94 - 24 * q^95 - 48 * q^96 + 16 * q^97 + 80 * q^98 - 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(131))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		131
131.2.a.a	$131$	$2$	131.a	1.a	$1$	$1$	$1$	$1.046$	\(\Q\)	None	✓	✓	✓	✓	131.2.a.a	$1$	$1$	\(0\)	\(-1\)	\(-2\)	\(-1\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-2q^{5}-q^{7}-2q^{9}+2q^{12}+\cdots\)
131.2.a.b	$131$	$2$	131.a	1.a	$1$	$10$	$10$	$1.046$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	✓	✓	✓	✓	131.2.a.b	$1$	$0$	\(0\)	\(1\)	\(4\)	\(1\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)