Space of modular forms of level 370, weight 2, and Character 370.ba

• Label: 370.2.ba
• Level: $370$
• Weight: $2$
• Character orbit: 370.ba
• Rep. character: $\chi_{370}(17,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $228$
• Newform subspaces: $2$
• Sturm bound: $114$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$370 = 2 \cdot 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	370.ba (of order $36$ and degree $12$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$185$
Character field:			$\Q(\zeta_{36})$
Newform subspaces:			$2$
Sturm bound:			$114$
Trace bound:			$1$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(370, [\chi])$.

	Total	New	Old
Modular forms	732	228	504
Cusp forms	636	228	408
Eisenstein series	96	0	96

Trace form

228 * q - 12 * q^3 + 6 * q^8 - 12 * q^12 + 24 * q^14 + 6 * q^20 - 12 * q^25 + 12 * q^27 - 48 * q^30 - 12 * q^33 - 84 * q^35 + 24 * q^37 - 24 * q^40 + 18 * q^41 + 84 * q^42 + 12 * q^44 - 120 * q^45 - 72 * q^49 - 60 * q^50 + 48 * q^53 + 72 * q^57 + 12 * q^58 - 108 * q^61 + 60 * q^62 - 114 * q^64 - 36 * q^65 - 84 * q^67 - 192 * q^69 - 24 * q^70 - 48 * q^71 - 6 * q^73 + 66 * q^74 + 192 * q^75 + 12 * q^76 - 60 * q^77 + 48 * q^79 + 12 * q^80 - 216 * q^81 + 96 * q^83 + 24 * q^86 + 216 * q^87 - 72 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 24 * q^93 - 108 * q^95 - 144 * q^97 + 24 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(370, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
370.2.ba.a	$370$	$2$	370.ba	185.z	$36$	$108$	$9$	$2.954$		None		✓			370.2.ba.a	$2$	$0$	$0$	$-6$	$6$	$0$		$\mathrm{SU}(2)[C_{36}]$
370.2.ba.b	$370$	$2$	370.ba	185.z	$36$	$120$	$10$	$2.954$		None		✓	✓		370.2.ba.b	$2$	$0$	$0$	$-6$	$-6$	$0$		$\mathrm{SU}(2)[C_{36}]$

Decomposition of $S_{2}^{\mathrm{old}}(370, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(370, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(185, [\chi])$$^{\oplus 2}$