Space of modular forms of level 51, weight 7, and Character 51.b

• Label: 51.7.b
• Level: $51$
• Weight: $7$
• Character orbit: 51.b
• Rep. character: $\chi_{51}(35,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	51.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(51, [\chi])\).

	Total	New	Old
Modular forms	38	32	6
Cusp forms	34	32	2
Eisenstein series	4	0	4

Trace form

32 * q + 32 * q^3 - 1024 * q^4 + 286 * q^6 + 568 * q^7 - 912 * q^9 - 744 * q^10 + 194 * q^12 - 2312 * q^13 - 6240 * q^15 + 13208 * q^16 + 2936 * q^18 + 7936 * q^19 - 21688 * q^21 + 13176 * q^22 + 18282 * q^24 - 76792 * q^25 + 87056 * q^27 + 45712 * q^28 - 45620 * q^30 - 36728 * q^31 + 73456 * q^33 - 52272 * q^36 + 133336 * q^37 - 48720 * q^39 - 81084 * q^40 - 305352 * q^42 - 412832 * q^43 - 9936 * q^45 + 283044 * q^46 + 233266 * q^48 + 342960 * q^49 + 50152 * q^52 + 196798 * q^54 + 7104 * q^55 - 22576 * q^57 + 167484 * q^58 - 58564 * q^60 - 235496 * q^61 - 331312 * q^63 + 299888 * q^64 + 485816 * q^66 - 774272 * q^67 + 553800 * q^69 - 1318656 * q^70 + 447312 * q^72 - 33152 * q^73 + 86872 * q^75 + 1045000 * q^76 - 8652 * q^78 + 1789576 * q^79 - 2391192 * q^81 - 178380 * q^82 - 751024 * q^84 + 235824 * q^85 - 155232 * q^87 - 3091500 * q^88 - 728056 * q^90 + 2080448 * q^91 + 1012816 * q^93 + 3173160 * q^94 + 422058 * q^96 - 1502960 * q^97 + 1619864 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(51, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
51.7.b.a	$51$	$7$	51.b	3.b	$2$	$32$	$32$	$11.733$		None		✓	✓	✓	51.7.b.a	$2$	$0$	\(0\)	\(32\)	\(0\)	\(568\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{7}^{\mathrm{old}}(51, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(51, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)