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

• Label: 35.4.f
• Level: $35$
• Weight: $4$
• Character orbit: 35.f
• Rep. character: $\chi_{35}(13,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

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

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 - 4 * q^2 - 10 * q^7 + 112 * q^8 - 56 * q^11 - 340 * q^15 - 248 * q^16 + 152 * q^18 + 468 * q^21 + 156 * q^22 - 308 * q^23 - 300 * q^25 - 528 * q^28 + 1460 * q^30 + 432 * q^32 + 90 * q^35 + 344 * q^36 + 116 * q^37 - 1580 * q^42 + 572 * q^43 - 912 * q^46 - 700 * q^50 - 944 * q^51 + 1420 * q^53 + 2648 * q^56 - 3200 * q^57 - 4348 * q^58 - 2000 * q^60 + 1830 * q^63 + 1660 * q^65 + 3396 * q^67 - 1020 * q^70 + 2704 * q^71 + 8936 * q^72 - 4024 * q^77 + 6860 * q^78 - 3164 * q^81 - 1460 * q^85 - 12872 * q^86 - 3584 * q^88 + 4268 * q^91 - 6328 * q^92 - 4480 * q^93 + 3400 * q^95 + 4092 * q^98

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.f.a	$35$	$4$	35.f	35.f	$4$	$4$	$2$	$2.065$	\(\Q(i, \sqrt{5})\)	None		✓			35.4.f.a	$4$	$0$	\(-8\)	\(0\)	\(0\)	\(-42\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-2-2\beta _{2})q^{2}+(1+2\beta _{1}+\beta _{2})q^{3}+\cdots\)
35.4.f.b	$35$	$4$	35.f	35.f	$4$	$16$	$8$	$2.065$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		35.4.f.b	$4$	$0$	\(4\)	\(0\)	\(0\)	\(32\)	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{7}q^{2}-\beta _{8}q^{3}+(-4\beta _{3}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)