Space of modular forms of level 51, weight 4, and Character 51.d

• Label: 51.4.d
• Level: $51$
• Weight: $4$
• Character orbit: 51.d
• Rep. character: $\chi_{51}(16,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	51.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(51, [\chi])\).

	Total	New	Old
Modular forms	20	8	12
Cusp forms	16	8	8
Eisenstein series	4	0	4

Trace form

8 * q - 4 * q^2 + 36 * q^4 - 48 * q^8 - 72 * q^9 - 236 * q^13 + 72 * q^15 + 372 * q^16 - 160 * q^17 + 36 * q^18 + 76 * q^19 - 84 * q^21 + 380 * q^25 + 796 * q^26 - 504 * q^30 - 1208 * q^32 + 60 * q^33 + 100 * q^34 - 288 * q^35 - 324 * q^36 - 116 * q^38 + 588 * q^42 + 124 * q^43 - 472 * q^47 + 64 * q^49 + 1120 * q^50 - 84 * q^51 - 1944 * q^52 + 1944 * q^53 + 316 * q^55 + 1224 * q^59 + 1332 * q^60 - 1228 * q^64 + 1596 * q^66 + 920 * q^67 - 2480 * q^68 - 1464 * q^69 - 1872 * q^70 + 432 * q^72 + 456 * q^76 - 4360 * q^77 + 648 * q^81 - 336 * q^83 - 1500 * q^84 + 836 * q^85 + 6364 * q^86 - 900 * q^87 - 344 * q^89 - 1092 * q^93 + 1432 * q^94 + 3756 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(51, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
51.4.d.a	$51$	$4$	51.d	17.b	$2$	$8$	$8$	$3.009$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	51.4.d.a	$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}-\beta _{4}q^{3}+(5-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(51, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(51, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 2}\)