Space of modular forms of level 35, weight 2, and Character 35.e

• Label: 35.2.e
• Level: $35$
• Weight: $2$
• Character orbit: 35.e
• Rep. character: $\chi_{35}(11,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(35, [\chi])\).

	Total	New	Old
Modular forms	12	4	8
Cusp forms	4	4	0
Eisenstein series	8	0	8

Trace form

4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^7 + 12 * q^8 - 2 * q^10 - 4 * q^11 + 6 * q^12 - 8 * q^13 - 4 * q^14 + 4 * q^15 - 6 * q^16 - 4 * q^17 + 8 * q^18 + 4 * q^20 + 14 * q^21 - 8 * q^22 + 2 * q^23 - 2 * q^24 - 2 * q^25 + 12 * q^26 + 4 * q^27 - 22 * q^28 - 4 * q^29 + 2 * q^30 + 12 * q^31 + 6 * q^32 - 12 * q^33 + 24 * q^34 - 4 * q^35 - 32 * q^36 - 8 * q^38 - 4 * q^39 - 6 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 12 * q^44 - 2 * q^46 - 4 * q^47 + 12 * q^48 + 10 * q^49 + 4 * q^50 + 4 * q^51 + 20 * q^52 + 8 * q^53 - 6 * q^54 + 8 * q^55 + 18 * q^56 - 16 * q^57 + 2 * q^58 + 8 * q^59 + 6 * q^60 + 6 * q^61 - 24 * q^62 - 28 * q^64 + 4 * q^65 + 4 * q^66 - 22 * q^67 - 20 * q^68 - 12 * q^69 - 10 * q^70 - 16 * q^71 + 8 * q^72 - 4 * q^73 - 2 * q^75 + 32 * q^76 + 28 * q^77 + 8 * q^78 - 24 * q^79 - 6 * q^80 + 2 * q^81 + 18 * q^82 + 4 * q^83 + 12 * q^84 + 8 * q^85 - 6 * q^86 + 2 * q^87 - 4 * q^88 + 6 * q^89 - 16 * q^90 - 28 * q^91 + 12 * q^92 + 12 * q^93 - 4 * q^94 + 10 * q^96 + 24 * q^97 - 14 * q^98 + 32 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.2.e.a	$35$	$2$	35.e	7.c	$3$	$4$	$2$	$0.279$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		✓	✓	✓	35.2.e.a	$2$	$0$	\(-2\)	\(-2\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1}-\beta _{2})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)