Space of modular forms of level 37, weight 8, and Character 37.c

• Label: 37.8.c
• Level: $37$
• Weight: $8$
• Character orbit: 37.c
• Rep. character: $\chi_{37}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $42$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(25\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(37, [\chi])\).

	Total	New	Old
Modular forms	46	46	0
Cusp forms	42	42	0
Eisenstein series	4	4	0

Trace form

42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(37, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
37.8.c.a	$37$	$8$	37.c	37.c	$3$	$42$	$21$	$11.558$		None		✓	✓	✓	37.8.c.a	$2$	$0$	\(-16\)	\(-68\)	\(-337\)	\(-158\)		$\mathrm{SU}(2)[C_{3}]$