Space of modular forms of level 35, weight 2, and trivial character

• Label: 35.2.a
• Level: $35$
• Weight: $2$
• Character orbit: 35.a
• Rep. character: $\chi_{35}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(35))\).

	Total	New	Old
Modular forms	6	3	3
Cusp forms	3	3	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.

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

Trace form

3 * q - q^2 + 3 * q^4 + q^5 - 8 * q^6 - q^7 - 9 * q^8 + q^9 - q^10 - 2 * q^11 + 4 * q^12 + 10 * q^13 + q^14 - 2 * q^15 + 7 * q^16 - 2 * q^17 + 7 * q^18 - 4 * q^19 + 7 * q^20 + 2 * q^21 + 8 * q^22 - 8 * q^23 - 4 * q^24 + 3 * q^25 + 6 * q^26 - 12 * q^27 - 7 * q^28 + 4 * q^29 - 8 * q^30 - 4 * q^31 - 9 * q^32 - 12 * q^33 - 6 * q^34 - 3 * q^35 + 3 * q^36 + 14 * q^37 + 20 * q^38 - 6 * q^39 - 9 * q^40 - 10 * q^41 + 8 * q^42 + 5 * q^45 - 16 * q^46 + 4 * q^47 + 28 * q^48 + 3 * q^49 - q^50 + 14 * q^51 - 6 * q^52 + 10 * q^53 + 12 * q^54 + 4 * q^55 + 9 * q^56 - 12 * q^57 - 26 * q^58 - 8 * q^59 + 8 * q^60 + 14 * q^61 - 5 * q^63 - q^64 - 4 * q^66 - 10 * q^68 + 12 * q^69 + q^70 + 16 * q^71 - 5 * q^72 - 6 * q^73 - 6 * q^74 - 36 * q^76 - 4 * q^77 - 20 * q^78 - 10 * q^79 - q^80 - 13 * q^81 - 18 * q^82 + 20 * q^83 - 8 * q^84 - 8 * q^85 + 12 * q^86 + 28 * q^87 + 4 * q^88 - 6 * q^89 + 7 * q^90 + 24 * q^92 - 4 * q^93 + 28 * q^94 - 8 * q^95 - 4 * q^96 - 10 * q^97 - q^98 + 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	7
35.2.a.a	$35$	$2$	35.a	1.a	$1$	$1$	$1$	$0.279$	\(\Q\)	None	✓	✓	✓	✓	35.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+q^{7}-2q^{9}-3q^{11}+\cdots\)
35.2.a.b	$35$	$2$	35.a	1.a	$1$	$2$	$2$	$0.279$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	35.2.a.b	$1$	$0$	\(-1\)	\(-1\)	\(2\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+(-1+\beta )q^{3}+(2+\beta )q^{4}+q^{5}+\cdots\)