Space of modular forms of level 35, weight 4, and Character 35.j

• Label: 35.4.j
• Level: $35$
• Weight: $4$
• Character orbit: 35.j
• Rep. character: $\chi_{35}(4,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(35, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

20 * q + 30 * q^4 + 3 * q^5 - 96 * q^6 + 82 * q^9 - 32 * q^10 + 36 * q^11 + 26 * q^14 - 146 * q^15 - 22 * q^16 - 192 * q^19 + 584 * q^20 - 404 * q^21 - 444 * q^24 - 187 * q^25 + 434 * q^26 + 260 * q^29 - 658 * q^30 + 834 * q^31 - 160 * q^34 + 661 * q^35 + 516 * q^36 + 868 * q^39 + 674 * q^40 - 1224 * q^41 + 542 * q^44 + 60 * q^45 - 1274 * q^46 - 326 * q^49 - 2556 * q^50 + 986 * q^51 - 2808 * q^54 - 742 * q^55 - 36 * q^56 - 2514 * q^59 - 204 * q^60 + 512 * q^61 + 6900 * q^64 - 946 * q^65 + 1396 * q^66 + 3064 * q^69 + 5190 * q^70 - 2944 * q^71 + 1590 * q^74 + 3003 * q^75 + 44 * q^76 + 46 * q^79 + 2304 * q^80 - 130 * q^81 - 12952 * q^84 - 5082 * q^85 - 1592 * q^86 - 5876 * q^89 - 3316 * q^90 + 4348 * q^91 - 3314 * q^94 - 2155 * q^95 + 3756 * q^96 + 13860 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.4.j.a	$35$	$4$	35.j	35.j	$6$	$20$	$10$	$2.065$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	35.4.j.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}-\beta _{14}q^{3}+(-\beta _{2}-3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)