Space of modular forms of level 392, weight 2, and Character 392.u

• Label: 392.2.u
• Level: $392$
• Weight: $2$
• Character orbit: 392.u
• Rep. character: $\chi_{392}(27,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $324$
• Newform subspaces: $1$
• Sturm bound: $112$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$392 = 2^{3} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	392.u (of order $14$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$392$
Character field:			$\Q(\zeta_{14})$
Newform subspaces:			$1$
Sturm bound:			$112$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(392, [\chi])$.

	Total	New	Old
Modular forms	348	348	0
Cusp forms	324	324	0
Eisenstein series	24	24	0

Trace form

324 * q - 5 * q^2 - 14 * q^3 - 5 * q^4 - 7 * q^6 - 11 * q^8 + 40 * q^9 - 7 * q^10 - 10 * q^11 + 28 * q^12 - 45 * q^14 + 3 * q^16 - 14 * q^17 - 24 * q^18 - 7 * q^20 + 11 * q^22 - 49 * q^24 - 56 * q^25 - 7 * q^26 - 14 * q^27 + 20 * q^28 - 28 * q^30 - 25 * q^32 - 14 * q^33 + 21 * q^34 + 10 * q^35 + 17 * q^36 + 7 * q^38 - 63 * q^40 - 14 * q^41 + 17 * q^42 - 10 * q^43 - 39 * q^44 + 21 * q^46 - 20 * q^49 + 104 * q^50 - 62 * q^51 - 7 * q^52 - 28 * q^54 - 62 * q^56 + 4 * q^57 - 11 * q^58 - 14 * q^59 - 59 * q^60 - 21 * q^62 - 35 * q^64 + 10 * q^65 - 35 * q^66 - 48 * q^67 + 39 * q^70 - 92 * q^72 - 14 * q^73 - 59 * q^74 - 14 * q^75 + 126 * q^76 - 27 * q^78 - 100 * q^81 - 112 * q^82 - 14 * q^83 + 22 * q^84 - 87 * q^86 + 35 * q^88 - 14 * q^89 - 126 * q^90 + 130 * q^91 + 66 * q^92 - 154 * q^94 + 238 * q^96 - 57 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(392, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
392.2.u.a	$392$	$2$	392.u	392.u	$14$	$324$	$54$	$3.130$		None		✓	✓	✓	392.2.u.a	$4$	$0$	$-5$	$-14$	$0$	$0$		$\mathrm{SU}(2)[C_{14}]$