Space of modular forms of level 399, weight 2, and Character 399.bc

• Label: 399.2.bc
• Level: $399$
• Weight: $2$
• Character orbit: 399.bc
• Rep. character: $\chi_{399}(248,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $106$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$399 = 3 \cdot 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	399.bc (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$106$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(399, [\chi])$.

	Total	New	Old
Modular forms	116	96	20
Cusp forms	100	96	4
Eisenstein series	16	0	16

Trace form

96 * q + 48 * q^4 - 4 * q^7 - 8 * q^9 - 12 * q^10 - 30 * q^12 + 8 * q^15 - 32 * q^16 - 2 * q^18 + 8 * q^21 - 48 * q^22 + 36 * q^24 - 60 * q^25 - 8 * q^28 - 28 * q^30 + 12 * q^31 - 6 * q^33 - 16 * q^36 - 16 * q^39 + 24 * q^40 - 12 * q^42 - 36 * q^45 - 12 * q^46 + 4 * q^49 + 18 * q^51 + 36 * q^52 - 36 * q^54 - 12 * q^58 + 8 * q^60 - 72 * q^61 + 8 * q^63 - 8 * q^64 + 48 * q^66 + 8 * q^67 + 64 * q^70 + 16 * q^72 + 24 * q^73 + 30 * q^75 + 12 * q^78 - 44 * q^79 - 36 * q^82 - 84 * q^84 - 56 * q^85 + 24 * q^87 - 4 * q^88 + 36 * q^91 + 48 * q^93 - 36 * q^94 + 168 * q^96 - 24 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(399, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
399.2.bc.a	$399$	$2$	399.bc	21.g	$6$	$96$	$48$	$3.186$		None		✓	✓	✓	399.2.bc.a	$4$	$0$	$0$	$0$	$0$	$-4$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{2}^{\mathrm{old}}(399, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(399, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(21, [\chi])$$^{\oplus 2}$