Space of modular forms of level 76, weight 2, and Character 76.f

• Label: 76.2.f
• Level: $76$
• Weight: $2$
• Character orbit: 76.f
• Rep. character: $\chi_{76}(27,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $20$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 76 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(20\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(76, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	16	16	0
Eisenstein series	8	8	0

Trace form

16 * q - 3 * q^2 - 3 * q^4 - 2 * q^5 + 5 * q^6 - 4 * q^9 - 6 * q^10 - 18 * q^13 - 6 * q^14 - 3 * q^16 + 2 * q^17 + 4 * q^20 + 3 * q^22 - 23 * q^24 - 2 * q^25 - 24 * q^26 - 4 * q^28 - 6 * q^29 + 28 * q^30 + 27 * q^32 + 18 * q^33 + 36 * q^34 + 14 * q^36 - 24 * q^38 + 48 * q^40 - 48 * q^41 + 28 * q^42 - 25 * q^44 + 24 * q^45 + 9 * q^48 + 16 * q^49 + 6 * q^52 + 6 * q^53 + 17 * q^54 - 26 * q^57 - 40 * q^58 - 6 * q^60 - 26 * q^61 + 32 * q^62 - 18 * q^64 + 5 * q^66 - 36 * q^68 - 54 * q^70 - 66 * q^72 + 16 * q^73 - 2 * q^74 + 43 * q^76 + 80 * q^77 - 84 * q^78 - 30 * q^80 + 12 * q^81 + 11 * q^82 + 14 * q^85 - 48 * q^86 + 18 * q^89 - 18 * q^90 - 52 * q^92 - 20 * q^93 + 46 * q^96 - 12 * q^97 + 51 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(76, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.2.f.a	$76$	$2$	76.f	76.f	$6$	$16$	$8$	$0.607$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	76.2.f.a	$4$	$0$	\(-3\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)