Space of modular forms of level 213, weight 2, and Character 213.l

• Label: 213.2.l
• Level: $213$
• Weight: $2$
• Character orbit: 213.l
• Rep. character: $\chi_{213}(23,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $132$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$213 = 3 \cdot 71$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	213.l (of order $14$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$213$
Character field:			$\Q(\zeta_{14})$
Newform subspaces:			$1$
Sturm bound:			$48$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(213, [\chi])$.

	Total	New	Old
Modular forms	156	156	0
Cusp forms	132	132	0
Eisenstein series	24	24	0

Trace form

132 * q - 10 * q^3 + 10 * q^4 - 15 * q^6 - 14 * q^7 - 14 * q^9 + 2 * q^10 + 20 * q^12 - 14 * q^13 + 22 * q^15 - 30 * q^16 + 8 * q^18 - 14 * q^19 - 28 * q^21 - 14 * q^22 + 8 * q^24 - 84 * q^25 - 7 * q^27 - 42 * q^28 - 5 * q^30 + 14 * q^31 - 7 * q^33 - 42 * q^34 - 43 * q^36 + 22 * q^37 - 35 * q^39 + 64 * q^40 - 28 * q^42 + 16 * q^43 - 50 * q^45 + 55 * q^48 + 12 * q^49 - 98 * q^51 - 168 * q^52 - 38 * q^54 + 70 * q^55 + 48 * q^57 + 86 * q^58 + 116 * q^60 + 14 * q^61 + 105 * q^63 + 2 * q^64 - 42 * q^67 - 28 * q^69 + 266 * q^72 - 62 * q^73 + 18 * q^75 - 120 * q^76 + 21 * q^78 - 74 * q^79 - 22 * q^81 - 182 * q^82 + 42 * q^84 - 2 * q^87 + 15 * q^90 - 22 * q^91 + 14 * q^94 - 210 * q^96 - 42 * q^97 + 49 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(213, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
213.2.l.a	$213$	$2$	213.l	213.l	$14$	$132$	$22$	$1.701$		None		✓	✓	✓	213.2.l.a	$4$	$0$	$0$	$-10$	$0$	$-14$		$\mathrm{SU}(2)[C_{14}]$