Space of modular forms of level 76, weight 3, and Character 76.b

• Label: 76.3.b
• Level: $76$
• Weight: $3$
• Character orbit: 76.b
• Rep. character: $\chi_{76}(39,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(76, [\chi])\).

	Total	New	Old
Modular forms	22	18	4
Cusp forms	18	18	0
Eisenstein series	4	0	4

Trace form

18 * q - 2 * q^2 - 6 * q^4 - 4 * q^5 - 6 * q^6 - 8 * q^8 - 54 * q^9 - 8 * q^10 + 16 * q^12 + 12 * q^13 + 36 * q^14 + 26 * q^16 + 20 * q^17 + 22 * q^18 + 40 * q^20 - 16 * q^21 - 24 * q^22 - 98 * q^24 + 46 * q^25 + 26 * q^26 + 6 * q^28 - 4 * q^29 - 84 * q^30 + 8 * q^32 - 48 * q^33 - 68 * q^34 + 68 * q^36 + 76 * q^37 - 180 * q^40 + 100 * q^41 + 202 * q^42 + 24 * q^44 - 68 * q^45 + 52 * q^46 + 248 * q^48 - 46 * q^49 - 190 * q^50 - 204 * q^52 + 12 * q^53 - 146 * q^54 + 12 * q^56 - 14 * q^58 - 52 * q^60 - 100 * q^61 + 300 * q^62 + 138 * q^64 - 88 * q^65 + 36 * q^66 + 58 * q^68 - 160 * q^69 + 36 * q^70 + 192 * q^72 - 268 * q^73 - 200 * q^74 + 296 * q^77 + 508 * q^78 - 316 * q^80 + 242 * q^81 - 276 * q^82 - 260 * q^84 + 176 * q^85 - 268 * q^86 + 472 * q^88 + 20 * q^89 + 316 * q^90 + 114 * q^92 + 80 * q^93 - 376 * q^94 - 10 * q^96 + 260 * q^97 - 106 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(76, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.3.b.a	$76$	$3$	76.b	4.b	$2$	$4$	$4$	$2.071$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		✓			76.3.b.a	$2$	$0$	\(-4\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
76.3.b.b	$76$	$3$	76.b	4.b	$2$	$14$	$14$	$2.071$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓	✓		76.3.b.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{5}q^{4}+\beta _{12}q^{5}+\cdots\)