Space of modular forms of level 35, weight 5, and Character 35.h

• Label: 35.5.h
• Level: $35$
• Weight: $5$
• Character orbit: 35.h
• Rep. character: $\chi_{35}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(35, [\chi])\).

	Total	New	Old
Modular forms	36	20	16
Cusp forms	28	20	8
Eisenstein series	8	0	8

Trace form

20 * q + 6 * q^2 - 18 * q^3 - 58 * q^4 - 54 * q^7 - 372 * q^8 + 266 * q^9 + 90 * q^11 + 1266 * q^12 - 690 * q^14 + 100 * q^15 - 126 * q^16 - 864 * q^17 - 848 * q^18 - 1662 * q^19 + 1680 * q^21 + 2584 * q^22 - 1242 * q^23 + 1908 * q^24 + 1250 * q^25 - 1350 * q^26 - 134 * q^28 + 840 * q^29 + 800 * q^30 - 3636 * q^31 - 1758 * q^32 + 384 * q^33 + 150 * q^35 - 4164 * q^36 + 1068 * q^37 + 9180 * q^38 + 2976 * q^39 - 4146 * q^42 - 7692 * q^43 - 3618 * q^44 - 1800 * q^45 + 2038 * q^46 - 11412 * q^47 + 416 * q^49 + 1500 * q^50 + 6324 * q^51 - 7476 * q^52 + 1668 * q^53 + 33180 * q^54 + 13500 * q^56 + 15264 * q^57 + 1174 * q^58 + 216 * q^59 - 8250 * q^60 - 5856 * q^61 - 23632 * q^63 - 25788 * q^64 - 4650 * q^65 - 16248 * q^66 + 34 * q^67 - 6444 * q^68 + 900 * q^70 + 10488 * q^71 - 12052 * q^72 + 22776 * q^73 + 2538 * q^74 - 2250 * q^75 + 40488 * q^77 + 23784 * q^78 + 20788 * q^79 + 14400 * q^80 + 4154 * q^81 - 34146 * q^82 - 20316 * q^84 + 12000 * q^85 + 1980 * q^86 - 27474 * q^87 - 36148 * q^88 - 13176 * q^89 + 17976 * q^91 + 61404 * q^92 - 22908 * q^93 - 50610 * q^94 - 6900 * q^95 - 17460 * q^96 - 39606 * q^98 - 36716 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(35, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
35.5.h.a	$35$	$5$	35.h	7.d	$6$	$20$	$10$	$3.618$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	35.5.h.a	$2$	$0$	\(6\)	\(-18\)	\(0\)	\(-54\)	$5^{4}\cdot 7^{3}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{1}+\beta _{3}+\beta _{4})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(35, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(35, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)