Space of modular forms of level 35, weight 3, and Character 35.i

• Label: 35.3.i
• Level: $35$
• Weight: $3$
• Character orbit: 35.i
• Rep. character: $\chi_{35}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(35, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

Trace form

12 * q + 6 * q^4 - 18 * q^9 - 54 * q^10 + 6 * q^11 - 66 * q^14 + 48 * q^15 - 6 * q^16 + 18 * q^19 + 12 * q^21 + 216 * q^24 + 18 * q^25 + 18 * q^26 + 48 * q^30 - 108 * q^31 + 222 * q^35 - 204 * q^36 - 240 * q^39 - 162 * q^40 - 42 * q^44 - 216 * q^45 + 114 * q^46 - 324 * q^49 - 192 * q^50 + 180 * q^51 + 252 * q^54 + 336 * q^56 + 396 * q^59 + 384 * q^60 - 108 * q^61 + 372 * q^64 - 54 * q^65 - 108 * q^66 + 300 * q^70 + 192 * q^71 - 594 * q^74 - 216 * q^75 - 192 * q^79 - 504 * q^80 + 294 * q^81 - 1200 * q^84 - 192 * q^85 - 384 * q^86 + 684 * q^89 - 72 * q^91 + 990 * q^94 + 288 * q^95 - 540 * q^96 + 396 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.3.i.a	$35$	$3$	35.i	35.i	$6$	$12$	$6$	$0.954$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	35.3.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)