Space of modular forms of level 91, weight 2, and trivial character

• Label: 91.2.a
• Level: $91$
• Weight: $2$
• Character orbit: 91.a
• Rep. character: $\chi_{91}(1,\cdot)$
• Character field: $\Q$
• Dimension: $7$
• Newform subspaces: $4$
• Sturm bound: $18$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(91))\).

	Total	New	Old
Modular forms	10	7	3
Cusp forms	7	7	0
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.

\(7\)	\(13\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(1\)	\(0\)		\(1\)	\(1\)	\(0\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(4\)	\(3\)	\(1\)		\(3\)	\(3\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(2\)	\(1\)	\(1\)		\(1\)	\(1\)	\(0\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(3\)	\(2\)	\(1\)		\(2\)	\(2\)	\(0\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(7\)	\(5\)	\(2\)		\(5\)	\(5\)	\(0\)		\(2\)	\(0\)	\(2\)

Trace form

7 * q - q^2 - 4 * q^3 + 3 * q^4 + 2 * q^5 - q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 - 4 * q^11 - 8 * q^12 + q^13 + q^14 - 4 * q^15 - 9 * q^16 + 2 * q^17 - 9 * q^18 - 12 * q^19 - 2 * q^20 - 4 * q^22 + 10 * q^23 - 4 * q^24 + 15 * q^25 + 3 * q^26 - 4 * q^27 - 7 * q^28 + 16 * q^29 + 8 * q^30 - 4 * q^31 + 15 * q^32 - 4 * q^33 + 2 * q^34 + 4 * q^35 - 9 * q^36 - 6 * q^37 - 8 * q^38 - 4 * q^39 - 10 * q^40 + 2 * q^41 - 8 * q^42 - 2 * q^43 + 22 * q^45 - 16 * q^46 + 8 * q^47 + 12 * q^48 + 7 * q^49 + q^50 + 8 * q^51 - q^52 - 16 * q^53 + 48 * q^54 + 12 * q^55 - 3 * q^56 + 30 * q^58 + 16 * q^59 - 20 * q^60 - 14 * q^61 - 8 * q^62 - 5 * q^63 - 17 * q^64 - 4 * q^65 + 12 * q^66 - 16 * q^67 + 42 * q^68 - 20 * q^69 + 6 * q^70 - 32 * q^71 - q^72 - 22 * q^73 + 26 * q^74 - 48 * q^75 + 16 * q^76 + 4 * q^77 + 8 * q^78 + 2 * q^79 - 38 * q^80 - 9 * q^81 + 14 * q^82 + 24 * q^83 + 16 * q^84 - 8 * q^85 - 24 * q^86 - 16 * q^87 + 36 * q^88 + 26 * q^89 - 50 * q^90 - 3 * q^91 - 12 * q^92 - 20 * q^93 - 20 * q^94 + 6 * q^95 - 4 * q^96 - 6 * q^97 - q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(91))\) 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	13
91.2.a.a	$91$	$2$	91.a	1.a	$1$	$1$	$1$	$0.727$	\(\Q\)	None	✓	✓	✓	✓	91.2.a.a	$1$	$1$	\(-2\)	\(0\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-3q^{5}-q^{7}-3q^{9}+\cdots\)
91.2.a.b	$91$	$2$	91.a	1.a	$1$	$1$	$1$	$0.727$	\(\Q\)	None	✓	✓	✓	✓	91.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(-3\)	\(1\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}-2q^{4}-3q^{5}+q^{7}+q^{9}+4q^{12}+\cdots\)
91.2.a.c	$91$	$2$	91.a	1.a	$1$	$2$	$2$	$0.727$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	91.2.a.c	$1$	$0$	\(0\)	\(0\)	\(6\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}+(3+\beta )q^{5}-2q^{6}+q^{7}+\cdots\)
91.2.a.d	$91$	$2$	91.a	1.a	$1$	$3$	$3$	$0.727$	3.3.316.1	None	✓	✓	✓	✓	91.2.a.d	$1$	$0$	\(1\)	\(-2\)	\(2\)	\(-3\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)