Space of modular forms of level 51, weight 2, and Character 51.e

• Label: 51.2.e
• Level: $51$
• Weight: $2$
• Character orbit: 51.e
• Rep. character: $\chi_{51}(4,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(51, [\chi])\).

	Total	New	Old
Modular forms	16	8	8
Cusp forms	8	8	0
Eisenstein series	8	0	8

Trace form

8 * q - 12 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^13 + 24 * q^14 + 12 * q^16 - 4 * q^17 - 4 * q^18 - 12 * q^20 - 8 * q^21 + 12 * q^22 - 16 * q^23 - 16 * q^24 - 8 * q^28 + 4 * q^29 + 24 * q^30 - 8 * q^31 + 12 * q^33 - 12 * q^34 + 8 * q^35 + 8 * q^37 + 24 * q^38 + 8 * q^39 + 36 * q^40 + 28 * q^41 - 32 * q^44 + 4 * q^45 - 20 * q^46 - 8 * q^47 - 32 * q^48 - 60 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^54 - 4 * q^55 - 24 * q^56 - 4 * q^58 + 16 * q^61 + 16 * q^62 - 4 * q^63 + 4 * q^64 + 16 * q^65 + 8 * q^67 + 60 * q^68 - 12 * q^69 + 24 * q^71 + 12 * q^72 + 20 * q^73 - 28 * q^74 - 16 * q^75 + 20 * q^78 + 20 * q^79 + 60 * q^80 - 8 * q^81 - 40 * q^82 + 48 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^88 - 8 * q^89 - 36 * q^91 + 56 * q^92 + 8 * q^95 + 8 * q^96 - 12 * q^97 - 76 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(51, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
51.2.e.a	$51$	$2$	51.e	17.c	$4$	$8$	$4$	$0.407$	8.0.836829184.2	None		✓	✓	✓	51.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)