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

• Label: 35.4.b
• Level: $35$
• Weight: $4$
• Character orbit: 35.b
• Rep. character: $\chi_{35}(29,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
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	14	10	4
Cusp forms	10	10	0
Eisenstein series	4	0	4

Trace form

10 * q - 36 * q^4 + 6 * q^5 + 12 * q^6 - 46 * q^9 - 16 * q^10 + 84 * q^11 - 56 * q^14 + 8 * q^15 + 148 * q^16 + 72 * q^19 - 68 * q^20 + 140 * q^21 + 72 * q^24 - 362 * q^25 - 620 * q^26 + 88 * q^29 + 52 * q^30 + 120 * q^31 + 964 * q^34 - 28 * q^35 - 420 * q^36 + 212 * q^39 + 1396 * q^40 - 852 * q^41 - 1424 * q^44 - 510 * q^45 + 176 * q^46 - 490 * q^49 + 1644 * q^50 + 1276 * q^51 - 996 * q^54 - 1136 * q^55 + 588 * q^56 + 864 * q^59 - 1692 * q^60 - 884 * q^61 - 2724 * q^64 + 520 * q^65 + 1148 * q^66 + 4808 * q^69 + 756 * q^70 + 880 * q^71 + 3024 * q^74 + 720 * q^75 - 2672 * q^76 - 3580 * q^79 - 2316 * q^80 - 302 * q^81 - 1904 * q^84 + 1572 * q^85 + 2432 * q^86 - 1492 * q^89 - 7748 * q^90 + 476 * q^91 + 1652 * q^94 - 1628 * q^95 + 4080 * q^96 - 5304 * 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.b.a	$35$	$4$	35.b	5.b	$2$	$10$	$10$	$2.065$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓	✓	35.4.b.a	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{2}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-4+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)