Space of modular forms of level 2394, weight 2, and Character 2394.bo

• Label: 2394.2.bo
• Level: $2394$
• Weight: $2$
• Character orbit: 2394.bo
• Rep. character: $\chi_{2394}(125,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $960$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	2394.bo (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$399$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$960$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(2394, [\chi])$.

	Total	New	Old
Modular forms	992	96	896
Cusp forms	928	96	832
Eisenstein series	64	0	64

Trace form

96 * q + 48 * q^4 - 8 * q^7 - 48 * q^16 - 8 * q^22 - 8 * q^25 - 4 * q^28 - 96 * q^37 + 40 * q^43 - 32 * q^46 + 56 * q^49 - 32 * q^58 - 96 * q^64 - 24 * q^67 - 16 * q^70 - 40 * q^79 - 8 * q^85 - 16 * q^88 + 44 * q^91

Decomposition of $S_{2}^{\mathrm{new}}(2394, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2394.2.bo.a	$2394$	$2$	2394.bo	399.z	$6$	$96$	$48$	$19.116$		None		✓	✓	✓	2394.2.bo.a	$8$	$0$	$0$	$0$	$0$	$-8$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{2}^{\mathrm{old}}(2394, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(2394, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(399, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(798, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1197, [\chi])$$^{\oplus 2}$