Space of modular forms of level 920, weight 2, and Character 920.bn

• Label: 920.2.bn
• Level: $920$
• Weight: $2$
• Character orbit: 920.bn
• Rep. character: $\chi_{920}(19,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $1400$
• Newform subspaces: $2$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bn (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 920 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(920, [\chi])\).

	Total	New	Old
Modular forms	1480	1480	0
Cusp forms	1400	1400	0
Eisenstein series	80	80	0

Trace form

1400 * q - 22 * q^4 - 30 * q^6 + 96 * q^9 - 11 * q^10 - 44 * q^11 - 22 * q^14 - 14 * q^16 - 44 * q^19 - 11 * q^20 - 48 * q^24 - 18 * q^25 - 30 * q^26 - 11 * q^30 - 44 * q^34 - 38 * q^35 + 2 * q^36 - 11 * q^40 - 36 * q^41 + 110 * q^44 - 14 * q^46 + 80 * q^49 - 15 * q^50 - 44 * q^51 - 34 * q^54 - 22 * q^56 - 36 * q^59 - 11 * q^60 - 58 * q^64 - 22 * q^65 - 88 * q^66 - 14 * q^70 - 22 * q^74 - 30 * q^75 - 132 * q^76 + 88 * q^80 - 152 * q^81 - 22 * q^84 - 242 * q^86 - 44 * q^89 + 220 * q^90 - 110 * q^94 - 456 * q^96 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(920, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
920.2.bn.a	$920$	$2$	920.bn	920.an	$22$	$40$	$4$	$7.346$		\(\Q(\sqrt{-10}) \)		✓			920.2.bn.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{22}]$
920.2.bn.b	$920$	$2$	920.bn	920.an	$22$	$1360$	$136$	$7.346$		None		✓	✓		920.2.bn.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$