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

• Label: 35.5.i
• Level: $35$
• Weight: $5$
• Character orbit: 35.i
• Rep. character: $\chi_{35}(19,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(20\)
Trace bound:			\(0\)

Dimensions

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

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

Trace form

28 * q + 94 * q^4 - 30 * q^5 - 222 * q^9 + 390 * q^10 + 34 * q^11 - 258 * q^14 + 60 * q^15 - 206 * q^16 + 366 * q^19 - 1116 * q^21 - 288 * q^24 + 40 * q^25 + 474 * q^26 + 856 * q^29 - 1620 * q^30 - 5520 * q^31 - 2620 * q^35 + 11892 * q^36 + 1656 * q^39 + 6510 * q^40 - 1082 * q^44 + 7920 * q^45 - 5442 * q^46 + 8356 * q^49 - 15960 * q^50 - 2976 * q^51 + 4392 * q^54 + 11640 * q^56 - 13920 * q^59 - 5700 * q^60 - 24960 * q^61 - 45596 * q^64 + 5290 * q^65 + 10332 * q^66 - 26400 * q^70 + 38272 * q^71 + 31806 * q^74 + 41310 * q^75 + 22028 * q^79 + 48000 * q^80 - 29238 * q^81 + 62784 * q^84 - 33820 * q^85 - 21180 * q^86 - 12516 * q^89 + 4448 * q^91 - 89418 * q^94 - 28890 * q^95 - 27900 * q^96 - 3108 * 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.i.a	$35$	$5$	35.i	35.i	$6$	$28$	$14$	$3.618$		None		✓	✓	✓	35.5.i.a	$4$	$0$	\(0\)	\(0\)	\(-30\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$