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

• Label: 76.3.g
• Level: $76$
• Weight: $3$
• Character orbit: 76.g
• Rep. character: $\chi_{76}(7,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $3$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	44	44	0
Cusp forms	36	36	0
Eisenstein series	8	8	0

Trace form

36 * q - q^2 - 3 * q^4 - 2 * q^5 - 15 * q^6 + 2 * q^8 + 36 * q^9 + 8 * q^10 - 22 * q^12 + 6 * q^13 + 18 * q^14 + 13 * q^16 - 26 * q^17 - 28 * q^18 - 76 * q^20 - 8 * q^21 + 33 * q^22 + 17 * q^24 - 52 * q^25 - 104 * q^26 - 42 * q^28 - 2 * q^29 - 96 * q^30 + 19 * q^32 + 36 * q^33 + 44 * q^34 - 2 * q^36 - 88 * q^37 - 186 * q^38 + 30 * q^40 + 50 * q^41 + 86 * q^42 + 225 * q^44 + 56 * q^45 + 212 * q^46 - 113 * q^48 - 92 * q^49 + 418 * q^50 - 54 * q^52 + 6 * q^53 + 167 * q^54 + 276 * q^56 - 6 * q^57 + 80 * q^58 - 182 * q^60 - 146 * q^61 - 156 * q^62 + 438 * q^64 - 164 * q^65 - 45 * q^66 + 140 * q^68 - 428 * q^69 + 36 * q^70 - 294 * q^72 - 134 * q^73 - 232 * q^74 + 483 * q^76 + 352 * q^77 + 152 * q^78 - 110 * q^80 + 334 * q^81 - 357 * q^82 - 100 * q^84 + 346 * q^85 + 22 * q^86 - 718 * q^88 + 118 * q^89 - 64 * q^90 - 540 * q^92 + 184 * q^93 - 488 * q^94 - 506 * q^96 - 374 * q^97 + 271 * 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.g.a	$76$	$3$	76.g	76.g	$6$	$4$	$2$	$2.071$	\(\Q(\sqrt{-3}, \sqrt{-10})\)	None		✓			76.3.g.a	$2$	$0$	\(-4\)	\(6\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-2\beta _{2}q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(-4+\cdots)q^{4}+\cdots\)
76.3.g.b	$76$	$3$	76.g	76.g	$6$	$4$	$2$	$2.071$	\(\Q(\sqrt{-3}, \sqrt{-10})\)	None		✓			76.3.g.a	$2$	$0$	\(8\)	\(-6\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+4q^{4}+\cdots\)
76.3.g.c	$76$	$3$	76.g	76.g	$6$	$28$	$14$	$2.071$		None		✓	✓		76.3.g.c	$4$	$0$	\(-5\)	\(0\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$